WO2018160125A1

WO2018160125A1 - Frequency hopping pattern in a wireless communication system

Info

Publication number: WO2018160125A1
Application number: PCT/SE2018/050193
Authority: WO
Inventors: Dennis SUNDMAN; Helia Niroomand RAD; Miguel Lopez; Yi-Pin Eric Wang
Original assignee: Telefonaktiebolaget Lm Ericsson (Publ)
Priority date: 2017-02-28
Filing date: 2018-02-28
Publication date: 2018-09-07

Abstract

A radio node (12, 14, 400, 450) is configured for use in a wireless communication system. The radio node (12, 14, 400, 450) is configured to determine a frequency hopping pattern (18) based on a sequence constant. The frequency hopping pattern (18) comprises a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P. The one or more lines each have the same slope and at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant. The radio node (12, 14, 400, 450) may be further configured to transmit or receive according to the frequency hopping pattern (18).

Description

FREQUENCY HOPPING PATTERN IN A WIRELESS COMMUNICATION SYSTEM

RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent Application Serial Number 62/465, 146 filed on February 28, 2017, the entire contents of which are incorporated herein by reference.

TECHNICAL FIELD

The present application relates generally to a wireless communication system, and relates more specifically to a frequency hopping pattern in a wireless communication system.

BACKGROUND

Frequency hopping (FH) spread spectrum systems are widely used in multiple access communication systems, such as Global System for Mobile communications (GSM) and Bluetooth. In such FH systems, a transmission (e.g., of a given message) is made by sending some of the data for the transmission on multiple frequency channels, e.g., one at a time. The order in which the channels are used is determined by a frequency hopping pattern. In other words, a frequency hopping pattern determines the frequency in or on which a transmitter sends a transmission at any given time.

For example, one technology which uses frequency hopping is Bluetooth. In Bluetooth

Low Energy (BLE), there are 37 frequency channels available. Since 37 is a prime number, the following hopping algorithm is used: f_n+1 = f_n + hop) (mod 37). Here, f_n is the frequency channel chosen for the current transmission, hop is a parameter chosen at random when the connection between transmitter and receiver is established, and f_n+1 is the channel for the next transmission.

One metric in the design of FH spread-spectrum systems is the number of hits or collisions among different hopping patterns. Mutual interference happens when two or more transmitters send in the same frequency and at the same time. When this happens, a collision has occurred. Thus, it is desirable to minimize the number of collisions among any pair of FH patterns while the total number of the FH patterns remains relatively high. Moreover, since in many wireless systems the transmitters are not time synchronized, it is also desirable to minimize the collisions between any first FH pattern and any arbitrary cyclic shift of any second FH pattern.

Some contexts complicate the design of frequency hopping patterns to have these optimal collision properties. One such context involves frequency hopping in an unlicensed frequency band. Indeed, frequency hopping systems in the unlicensed frequency band may be subject to regulation. These regulations vary from region to region, and impose restrictions on the FH patterns. As an illustration, Figure 1 summarizes the regulations mandated by the Federal Communications Commission (FCC) for wireless systems operating in the band 902 MHz to 928 MHz. Constraints imposed by these regulations impose challenges in minimizing collisions and maximizing the number of frequency hopping patterns for the system. The constraints may for instance necessitate that a frequency hopping pattern have a certain length and/or period that is non-prime, and/or that any pair of patterns provides an average of equal use of the available channels.

SUMMARY

Embodiments include a radio node (e.g., a user equipment or a base station) configured to transmit or receive in a wireless communication system according to a frequency hopping pattern.

More particularly, embodiments include a method implemented by a radio node configured for use in a wireless communication system. The method may include determining a frequency hopping pattern based on a sequence constant. The frequency hopping pattern comprises a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P . The one or more lines each have the same slope and at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant. The method may further include transmitting or receiving according to the frequency hopping pattern. In some embodiments, the method may also include determining the sequence constant.

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, and P < N .

In some embodiments, the sequence constant is a function of a system frame number and/or a hyper system frame number in which the radio node is to transmit or receive according to the frequency hopping pattern. A hyper system frame comprises multiple system frame numbers.

In some embodiments, the sequence constant is the same as a sequence constant on which is based another frequency hopping pattern according to which another radio node is to transmit or receive.

In some embodiments, the sequence constant is included in a set of sequentially ordered sequence constants and is sequentially ordered after a previous sequence constant on which is based a frequency hopping pattern according to which the radio node previously transmitted or received.

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the N frequencies are indexed from an initial index to the initial index plus N . In this case, the sequence constant has a value that is greater than or equal to the initial index and that is less than or equal to the initial index plus N . In some embodiments, the method further comprises determining a sequence slope parameter, and determining the frequency hopping pattern based on the sequence slope parameter, wherein the one or more lines each have a slope equal to the sequence slope parameter.

In some embodiments, the method further comprises receiving signaling indicating assignment of the sequence slope parameter to the radio node.

In some embodiments, the frequency hopping pattern comprises a frequency sequence of length P with frequency indices corresponding to {(0 x p) + k, (1 x p) + k, (2 x p) +

k, [( - 1) x p] + k} in the Galois field GF(P), where k is the sequence constant and p is the slope. In some of these embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, and P < N .

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the frequency hopping pattern comprises a frequency sequence of length P with frequency indices corresponding to {[(0 x p) + k]mod N, [(1 x p) + k]mod N, [(2 x p) + k]mod N, ... , [[(P - 1) x p] + k]mod N} in the Galois field GF(P), where k is the sequence constant and p is the slope.

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the frequency hopping pattern comprises a frequency sequence sip, k) of length P with frequency indices corresponding to sip, k) =

{v₀imod Ν),

= {(0 x p) +

k, (1 x p) + k, (2 x p) + k, ... , [iP - 1) x p] + k] in the Galois field GF( ), where k is the sequence constant and p is the slope.

In some embodiments, P is prime. In other embodiments, P is a prime power.

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein N is a composite number.

In some embodiments, the method further comprises determining a different frequency hopping pattern that is based on a different sequence constant. The different frequency hopping pattern comprises a different frequency sequence of length P with frequency indices from one or more different lines in a finite affine plane over a Galois field with an order equal to P . The one or more different lines each have said same slope and wherein at least one of the one or different more lines is offset from the origin of the Galois field by a different sequence constant. The method in this case may further comprise switching from transmitting or receiving according to the frequency hopping pattern to transmitting or receiving according to the different frequency hopping pattern.

In some embodiments, the wireless communication system is a narrowband internet of things system. Alternatively or additionally, the transmitting or receiving according to the frequency hopping pattern may be performed in an unlicensed frequency band. Embodiments also include a method implemented by a radio node configured for use in a wireless communication system with N frequencies usable by a frequency hopping pattern. The method may comprise transmitting or receiving according to a frequency hopping pattern that comprises a frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P , where ^ > N . The multiple lines each have the same slope.

In some embodiments, at least one of the multiple lines is offset from the origin of the Galois field by a sequence constant. In some embodiments, the sequence constant is a function of a system frame number and/or a hyper system frame number in which the radio node is to transmit or receive according to the frequency hopping pattern. A hyper system frame comprises multiple system frame numbers.

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the N frequencies are indexed from an initial index to the initial index plus N . In this case, the sequence constant has a value that is greater than or equal to the initial index and that is less than or equal to the initial index plus N .

In some embodiments, the method further comprises determining a sequence slope parameter, and determining the frequency hopping pattern based on the sequence slope parameter, wherein the one or more lines each have a slope equal to the sequence slope parameter.

k, [(P - 1) x p] + k} in the Galois field GF(P), where k is the sequence constant and p is the slope.

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the frequency hopping pattern comprises a frequency sequence of length P with frequency indices corresponding to {[(0 x p) + k]mod N, [(1 x p) + k]mod N, [(2 x p) + k]mod N, [[(P - 1) x p] + k]mod N} in the Galois field GF(P), where k is the sequence constant and p is the slope.

In the same or other embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the frequency hopping pattern comprises a frequency sequence sip, k) of length P with frequency indices corresponding to s(p, k) = {v₀(mod N), v^mod N), ... ν_Ρ__± (mod N)}, where vector s = {v₀, v_±, ... v_P-_±} =

{(0 x p) + k, (1 x p) + k, (2 x p) + k, [(P - 1) x p] + k] in the Galois field GF(P), where k is the sequence constant and p is the slope.

In some embodiments, P is prime or a prime power.

In some embodiments, the wireless communication system is a narrowband internet of things system. Alternatively or additionally, the transmitting or receiving according to the frequency hopping pattern may be performed in an unlicensed frequency band.

Embodiments further include corresponding apparatus, computer programs, carriers, and computer program products.

For example, embodiments include a radio node configured for use in a wireless communication system. The radio node is configured to determine a frequency hopping pattern based on a sequence constant. The frequency hopping pattern comprises a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P . The one or more lines each have the same slope and at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant. The radio node may be further configured to transmit or receive according to the frequency hopping pattern. In some embodiments, the radio node may also be configured to determine the sequence constant.

Embodiments also include a radio node configured for use in a wireless communication system with N frequencies usable by a frequency hopping pattern. The radio node is configured to transmit or receive according to a frequency hopping pattern that comprises a frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P , where ^ > N . The multiple lines each have the same slope.

A frequency hopping pattern in some embodiments herein may advantageously have any (arbitrary) length. Some embodiments herein exploit a sequence constant, by transmitting or receiving at different times according to different frequency hopping patterns that are based on different sequence constants, in order to over time (on average) provide (substantially) equal use of available frequency channels. Alternatively or additionally, frequency hopping patterns used by different radio nodes herein are based on different slopes, so as to advantageously provide desired collision properties between the frequency hopping patterns used by different radio nodes

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a table of regulations mandated by the Federal Communications Commission for wireless systems according to some embodiments.

Figure 2 is a block diagram of a wireless communication system according to some embodiments.

Figure 3A is a diagram representing a frequency hopping sequence as a line in a finite affine plane over a Galois field according to some embodiments.

Figure 3B is a diagram representing a frequency hopping sequence as one or more lines in a finite affine plane over a Galois field according to some embodiments.

Figure 4 is a logic flow diagram of a method performed by a radio node according to some embodiments.

Figure 5 is a diagram representing different frequency hopping sequences based on different sequence constants according to some embodiments.

Figure 6 is a table showing collisions between two example frequency hopping patterns according to some embodiments.

Figure 7 is a logic flow diagram of an algorithm for generating and using frequency hopping patterns according to some embodiments.

Figure 8 is a logic flow diagram of an algorithm for generating and using frequency hopping patterns according to other embodiments.

Figure 9A is a diagram representing a line in a finite affine plane over a Galois field according to some embodiments.

Figure 9B is a diagram representing the line of Figure 9A as offset by a sequence constant according to some embodiments.

Figure 9C is a diagram representing the line of Figure 9A as offset to a greater extent by a sequence constant according to some embodiments. Figure 10A is a diagram representing a line in a finite affine plane over a Galois field according to some embodiments where P > N.

Figure 10B is a diagram representing the line of Figure 10A after a module N operation according to some embodiments.

Figure 10C is a diagram representing another line in a finite affine plane over a Galois field according to some embodiments where P > N.

Figure 10D is a diagram representing the line of Figure 10C after a module N operation according to some embodiments.

Figure 1 1 is a logic flow diagram of a method performed by a radio node according to other embodiments.

Figure 12 is a block diagram of frequency spectrum according to some embodiments.

Figure 13A is a block diagram of a radio node according to some embodiments.

Figure 13B is a block diagram of a radio node according to other embodiments.

Figure 14 is a block diagram of a user equipment according to some embodiments. Figure 15 is a block diagram of a radio network node according to some embodiments.

DETAILED DESCRIPTION

Figure 2 illustrates a wireless communication system 10 (e.g. , a narrowband loT, NB-loT, system) according to one or more embodiments. The system 10 includes radio nodes shown in the form of a radio network node 12 (e.g., an eNB) and a wireless communication device 14 (e.g. , a user equipment, which may be a NB-loT device).

One radio node (e.g. , device 14) may transmit a signal 16 to another radio node (e.g. , eNB) that receives that signal 16. Figure 2 shows that the signal 16 in this regard is transmitted and/or received according to a frequency hopping pattern 18 that hops the signal 16 from frequency to frequency over time. As illustrated, for instance, signal 16 is hopped from frequency fA to frequency fB over time according to a frequency hopping pattern 18 {fA, fB, . . . }, where A and B represent frequency indices that index frequencies within the system 10 over which the signal 16 may be hopped. The frequency hopping pattern 18 as shown therefore is represented as a frequency sequence fA, fB, . . . in which frequencies in the sequence have a respective index A, B, etc. In any event, hopping may be realized by one part 16A of the signal 16 (e.g., one symbol or symbol group) being transmitted or received on a time-frequency resource that occupies or is centered on frequency fA , and another part 16B of the signal 16 being transmitted or received on a time-frequency resource that occupies or is centered on frequency fB.

Figure 3A illustrates additional details of the frequency hopping pattern 18 according to some embodiments. As shown, the frequency hopping pattern 18 comprises a frequency sequence fi , f2, . . . fp of length P. That is, there are P frequency indices in the frequency sequence. The frequency indices in the sequence are from (i.e. , are included in or on) a line 20 in a finite affine plane over a Galois field GF(P) with an order equal to P. A Galois field as used herein is a field that contains a finite number of elements, where the number of elements in the field is called the order of the field. Figure 3A shows this line 20 as being formed from possible frequency indices 22 and as having a certain slope p. Regardless, a frequency hopping pattern 18 comprising frequency indices from such a line 20 may in some embodiments advantageously have any (arbitrary) length P (e.g. , such that P in some embodiments is prime, but in other embodiments may be a prime power, an odd number, or an even number).

Figure 3A furthermore shows that the line 20 in some embodiments is offset (i.e. , by a non-zero amount) from the origin of the Galois field GF(P) by a so-called sequence constant k. The sequence constant k may remain fixed while transmitting or receiving according to the frequency hopping pattern 18, i.e. , using the frequencies indexed by the pattern 18.

Although Figure 3A shows an example where the frequency indices in the sequence are from a single line in a finite affine plane over GF(P), in other embodiments the frequency indices are from one or more lines in a finite affine plane over GF(P). In Figure 3B, for instance, the frequency indices 22 in some sense may be from one line formed from line segments 20-1 and 20-2 but that line has a discontinuity 24. In another sense, though, the frequency indices 22 may be said as being from multiple lines 20-1 and 20-2 that each have the same slope p. In this case, at least one of these lines (e.g. , line 20-1 in Figure 3B) is offset from the origin of GF(P) by the sequence constant k.

Accordingly, Figure 4 illustrates a method 100 implemented by a radio node configured for use in a wireless communication system 10 according to some embodiments. The radio node may for instance be a radio network node 12 or a wireless communication device 14 (e.g., a user equipment). Optional steps are shown in dotted lines. The method 100 as shown includes determining a sequence constant (e.g., k as notated herein) (Block 1 10). The method 100 may also include determining a frequency hopping pattern 18 based on the sequence constant (Block 120). Such determination may comprise for instance generating the pattern 18 or selecting the pattern 18 from a set or table of patterns. Regardless, the frequency hopping pattern 18 may comprise a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P. The one or more lines each have the same slope (e.g., p as notated herein) and at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant. In some

embodiments, then, the frequency hopping pattern 18 may be based on the sequence constant in the sense that at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant. In any event, the method 100 may also include transmitting or receiving according to the frequency hopping pattern (Block 130).

As explained below, other frequency hopping sequences may have a different sequence constant, so as to be associated with a different offset from the origin of the Galois field GF(P). Figure 5 for example, shows a different frequency hopping pattern 24 that comprises a different frequency sequence fi , f2, ... fp of length P. The frequency indices in the sequence are from a different line 26 in a finite affine plane over the Galois field GF(P) . This different line 26 as shown has the same slope p as line 20, but is offset from the origin of GF(P) by a different sequence constant k2 (where k = kl for line 20 in Figure 5). This results in the different frequency hopping pattern 24 including other frequency indices 28 not included in pattern 18. Some embodiments thereby exploit the sequence constant, by transmitting or receiving at different times according to different frequency hopping patterns that are based on different sequence constants, in order to over time (on average) provide (substantially) equal use of the available frequency channels.

In fact, according to some embodiments, the sequence constant is a function of a system frame number (SFN) and/or a hyper system frame number (HFN) in which a radio node is to transmit or receive according to the frequency hopping pattern 18, e.g. , so that the sequence constant is in a sense synchronized with SFN and/or HFN. A system frame number in this regard indicates an index of one of multiple system frames that have different indices (e.g., from 0 to 1023). A hyper system frame comprises multiple system frames (e.g. , 1024 system frames). A hyper system frame number indicates an index of one of multiple hyper system frames that have different indices (e.g. , from 0 to 1023). In any event, this means that a radio node may transmit or receive according to different frequency hopping patterns (based on different sequence constants) in different SFNs and/or HFNs. Moreover, in these and other embodiments, the sequence constant on which is based one frequency hopping pattern according to which one radio node is to transmit or receive in a given SNF and/or HFN may be the same as the sequence constant on which is based another frequency hopping pattern according to which another radio node is to transmit or receive in that same SFN and/or H FN.

In view of these embodiments, the method 100 in Figure 4 in some embodiments further comprises determining the sequence constant as a function of a system frame number (SFN) and/or a hyper system frame number (HFN) in which the radio node is to transmit or receive according to the frequency hopping pattern. Again, a hyper system frame comprises multiple system frames (e.g. , 1024 system frames).

These and other embodiments may be realized using frequency hopping patterns that are based on sequentially ordered sequence constants. A frequency hopping pattern that a radio node is to use next may for instance be based on a sequence constant that is next in a set of sequentially ordered sequence constants after a previous sequence constant on which was based a previously used frequency hopping pattern, i.e. , the next sequence constant is sequentially ordered after the previous sequence constant in the set. In this case, for instance, the sequence constants on which are based frequency hopping patterns that are successively used may be increments of one another, e.g. , k1 =0; k2=1 ; k3=2, etc. Alternatively, in other embodiments, sequence constants may be randomly or pseudo randomly determined from a set of multiple sequence constants. No matter the particular way the sequence constant may govern the frequency hopping pattern, the method 100 in Figure 4 in some embodiments may further include determining a different frequency hopping pattern 24 based on a different sequence constant kl . This different frequency hopping pattern 24 may comprise a different frequency sequence of length P with frequency indices from one or more different lines in a finite affine plane over a Galois Field with an order equal to P. The one or more different lines each have said same slope p. At least one of the one or more different lines is offset from the origin of the Galois field by the difference sequence constant kl . The method 100 may further include switching from transmitting or receiving according to frequency hopping pattern 18 to transmitting or receiving according to the different frequency hopping pattern 24.

In some embodiments, different radio nodes in the system 10 transmit or receive according to different frequency hopping patterns. These different frequency hopping patterns may comprise different respective frequency sequences with frequency indices from one or more lines in a finite field over GF(P). But the line(s) associated with different patterns used by different radio nodes may have different slopes. In some embodiments, for instance, the slope may be specific to each radio node. In this case, each radio node may for example receive signaling indicating assignment of the slope (e.g., via a sequence slope parameter) to the radio node. No matter the way in which different slopes are associated with different radio nodes, such may advantageously provide desired collision properties between the frequency hopping patterns used by different radio nodes in the system 10.

In fact, in some embodiments, different radio nodes in the system 10 may transmit or receive according to different frequency hopping patterns that are associated with different slopes, even if one of the radio nodes itself uses different frequency hopping patterns associated with different slopes at different times. A radio node may for example select the next frequency hopping pattern to use during the next time period as a pattern associated with a slope that is different than both (i) the slope on which was based the frequency hopping pattern used by the radio node during the previous time period; and (ii) the slope on which is based another frequency hopping pattern used by another radio node during the next time period. That is, a radio node may select consecutive sequences based on different slopes, assuming no other radio node selects a sequence with the same slope for use at the same time.

Some embodiments in this regard address the challenge to provide frequency hopping (FH) sequences with the following properties. Among an arbitrary number of FH sequences generated, any pair of FH sequences provides an average of equal use of the available channels, and one or many FH sequences used by different transmitters are to be used without collision at all or with a good fraction of collision properties.

Consider for instance a performance measure defined in terms of a fraction of collisions between FH sequences representing FH patterns. Given two FH patterns a and b with period P a = {α(0), α(2), ... , a(P - 1)}, b = {Κ0), ΚΌ b(P - 1)1

the number of collisions H(a, b) between them can be quantified using the following expression:

H(a, b) = δ(α(ρ)— b(p + k (mod P)))

Here, x (mod P) denotes the modulus P operation and δ is the Kronecker delta:

The expression H(a, simply counts the number of collisions between the FH pattern a and all the cyclic shifts of the FH pattern b, and then chooses the maximum value. As an example, suppose that P = 4, and let

a = {2,0,1,3},

b = {1,3,0,2}.

For this example, the calculation of H(a, b) is visualized with the help of the table in Figure 5.

The numbers in bold indicate positions in the FH pattern where a and a cyclic shift of b coincide. The number of collisions is calculated as the maximum of the numbers in the last row of the table in Figure 6:

H(a, b) = max{0, 1, 2,1} = 2.

Given a set S of FH patterns, one can define a figure of merit H(S) by computing the maximum number of collisions among any pair of FH patterns in the set per the expression:

H(S) = max{H(a, b)}.

a.bes

To evaluate if a set S of FH patterns provides good properties, it is relevant to know the length of the FH patterns. If the length of the patterns is, for example 4, and H(S) = 2, it means that the maximum number of collisions of some pair of sequences with some shift is 50%.

Therefore, a function of merit is defined to be:

where P is the length of the sequences inside the set S. The function C(S) is referred to as the fraction of collisions, and for ease of understanding will be expressed in percent. For example, if the length of the sequences P = 47 and H(S) = 1, it means that the fraction of collisions C(S) « 2.1%.

Some embodiments include a method to create one or more FH sequences. In this regard, assume there are N channels where N is a composite number. Also, assume that P - 1 sequences of length P are to be constructed, where P may be a prime.

The method may be performed to generate one P length FH sequence that comprises a sequence of indices. The indices in the sequence may be selected from a set of possible indices that index frequencies within the system 10 over which frequency hopping may be performed. The set of possible indices is assumed in this example to include indices numbered from 0 to N - 1.

Figure 7 shows the method 200 as including the following steps. First, the method 200 includes choosing a sequence number p such that 1≤ p≤ P - 1 (Block 210). In some embodiments, each transmitter within communication range needs a unique p; that is, p is assumed unique to each transmitter. The chosen sequence number p may remain fixed in some embodiments. Second, the method 200 includes constructing the vector t = {0 x p, 1 x p, 2 x p, (P - 1) x p} in a Galois field with an order equal to P, i.e., GF(P) (Block 220). The sequence number p describes the slope of the vector t, such that the sequence number p may be referred to as a sequence slope parameter. This vector t, with its elements coming from the Galois field GF(P), may be geometrically demonstrated by a line in a finite affine plane over GF(P), where the vector elements are viewed as the points of the finite affine plane. From this perspective, the vector t in GF(P) is equivalent to a line in a finite affine plane over GF(P).

Third, the method 200 includes choosing a parameter k such that 0≤ k≤ N - 1 (Block 230). The parameter k may also be referred to herein as a sequence constant. The parameter k can be chosen freely, but in some embodiments it is assumed to be known to receivers. Fourth, the method 200 comprises constructing the vector v = {t₀ + k, t_t + k, ... t_P_₁ + k}, e.g., in integers (Block 240). The vector v therefore represents the vector t as shifted or offset by the parameter k. This shifting or offsetting, though, could cause the values of the resulting vector v to exceed the maximum frequency index N - 1 in the system 10. Accordingly, the method 200 further comprises creating a FH sequence s(p, k) by using the modulo N operation on each element, i.e., s(p, k) = {v₀(mod N),

N)} (Block 250). This effectively limits the indices of the FH sequence so that they are between 0 and the maximum frequency index N - 1.

The above procedure will generate one P length FH sequence s(p, k), which is dependent on P, N, p, k. A transmitter can use this sequence to select frequencies for transmission. For example, as shown in Figure 7, the transmitter may set a parameter t = 0 (Block 260) and perform a transmission (e.g., at a certain time) using a frequency channel s_t corresponding to the t'th index in the FH sequence s(p, k) (Block 270). For performing the transmission (e.g., at a later time), the transmitter may determine if t = P (Block 280) and, if not, increment t (Block 290) in order to perform the transmission (e.g., at a later time) using the frequency channel corresponding to the next index in the FH sequence s(p, k). When there are no more frequencies remaining in s(p, k) (i.e., YES at Block 280), the transmitter may generate a new sequence by running the algorithm from step 3 corresponding to Block 230. The new sequence may therefore be based on the same sequence number p (i.e., the same slope in GF(P)), but be based on a different sequence constant k (i.e., a different shift or offset).

There are some parameters chosen for the algorithm which requires some attention. Consider the choice of P. As already mentioned, the parameter is typically a prime. However, other numbers are also possible. Choosing P to be a prime may provide the best performance in terms of fraction of collisions, followed by choosing P to be a prime power (not power of 2 and not power by 1), followed again by choosing P to be an odd number, and worst is letting P be an even number.

Consider now the choice of p. In general, the described procedure can generate FH sequences which contain multiple consecutive instances of the same number (i.e., which suggest multiple consecutive channel uses of the same channel). This might be undesired in certain applications. However, only few (experiments suggest every Nth) sequence will have this property. Therefore, if multiple consecutive channel uses are undesirable, discarding these sequences may be performed. This is shown in Figure 8 as an example, where in a method 205 an additional step 255 is included (relative to the method 200 in Figure 7) to avoid using sequences with multiple consecutive channels. Naturally, if P < N, such sequences will not appear. Note that the sequences with multiple consecutive channel uses of the same channel is independent of k.

Consider next the choice of k. Experiment suggests that if k is chosen in coordination among the sets of frequencies, the fraction of collision becomes better. One such example of coordination is if all sets of frequencies choose the same k, i.e. s_t = s(p_lr k) and s₂ = s(p₂, k) for all p₁≠ p₂.

For a transmitter p in order to obtain equal channel usage (in average) over time, 9 sequences with different k's may be used. One way to select such k's is deterministically and sequentially, for example:

k₀ = 0, ki = 1, ... , k_N-i = N— l, k_N = 0, k_N+i = 1, ...

If k is chosen like this, the period of the sequences s(p_ir k_j) will be N x P. Another way is to select k uniformly at random between 0 and N.

An understanding of the algorithm according to some embodiments may be attained through recognizing the fact that using FH sequences by using lines with different slopes in GF(P) provides good fraction of collision properties.

Consider the case where P < N; that is, where the length of the FH sequences (P) is less than the number N of frequency channels in the system 10 available for frequency hopping. For the prime P, any two sequences where p₁≠ p₂

a = {0 X _Pl, 1 X _Pl, 2 X _Pl (P - 1) X _Pl] in GF(P)

¾ = {0xp₂,lx¾,2x p₂ (P - 1) X p₂} in GF(P)

will have a fraction of collisions C(a, b) = However, since P < N, not all channels are used in any of the above FH sequences. To illustrate this, consider the following example: Let N = 10,P = 7, p_t = l, p₂ = 2. In this case:

a = {0 X _Pl, 1 X _Pl, 2 X _Pl (P - 1) X _Pl] in GF(P) = {0,1,2,3,4,5,6} ¾ = {0 x ¾, l x p₂, 2 x p₂ (P - 1) X p₂} in GF(P) = {0,2,4,6,1,3,5}.

Neither sequence uses all 10 available channels.

To use all channels equally (in average over time), some embodiments advantageously exploit an additional parameter k. The parameter k will introduce a change to all the parameters such that, for example when k = 1, the sequences are modified to be:

a' = {a₀+k (mod N), a_± + k (mod N), ... , α_Ρ-_± + k (mod N)} = {1,2,3,4,5,6,7} b' = {b₀+k (mod N), b_t + k (mod N), ... , b_P_ + k (mod N)} = {1,3,5,7,2,4,6}. Note here that the maximal value in both a' and V is now 7. Since all sequences are

constructed as lines with different slopes in a finite affine plane over GF(P), this operation corresponds to a constant shift k of these lines, but with the same slope. Figures 9A and 9B show an example of this. Figure 9A shows sequence a as being a line with a certain slope in a finite affine plane over GF(P), whereas Figure 9B shows sequence a' as being a line with the same slope but the line is shifted relative to a. For larger values of k, the line will look as shown in Figure 9C, i.e., to have a discontinuity as a result of the modulo N operation. In some sense, then, Figure 9C shows that the sequence a" may be represented as multiple lines that have the same slope.

Studying these figures, using only one k for each FH pattern at a transmitter, not all N channels will be used where P < N. But by changing k between the FH patterns used at different times, all channels can be used over time. It can also be understood that when all transmitters use the same k, the good property C(a', b') = ^ will be kept. However, when the stations use, for example, random k's the worst case is C(a, c) = where c is for example generated by choosing p = 2 and finding the k providing worst C(a, c).

Consider now an example of two sequences where the length of the FH sequences (P) is greater than the number N of frequency channels in the system 10 available for frequency hopping. Let JV = 10, P = 13, p₁ = l, p₂ = 2. In this case, two sequences may be:

d = {0 X p_1; l X p_1; 2 x p_1; ... , (P - 1) X p_x} in GF(P) = {0,1,2,3,4,5,6,7,8,9,10,11,12}

e = {0 X p₂, 1 X p₂, 2 X p₂ (P - 1) X p₂} in (P) = {0,2,4,6,8,10,12,1,3,5,7,9,11}.

Then, where k = 1, the sequences may be shifted to become:

d' = {d₀+k (mod N), d₁ + k (mod N), ... , d_P_₁ + k (mod N)} = {1,2,3,4,5,6,7,8,9,0,1,2,3} e' = {e₀+k (mod N), e₁ + k (mod N), ... , e_P_ + k (mod N)} = {1,3,5,7,9,1,3,2,4,6,8,0,2}

Notice there are two "modulo" operations operating after each other. But a line with a certain slope is still being shifted. Since the sequence length now is longer than N, more collisions will occur.

Figures 10A-10D more particularly illustrate the effect of the second modulo N operation. Figure 10A shows a line a in a finite affine plane over GF(P) and Figure 10B shows the same line a after the module N operation as multiple lines in a finite affine plane over GF(P) that have the same slope. Observe that GF(P) in this case is only defined for prime P. Figures 10C and 10D show another example. Figure 10C shows a line b in a finite affine plane over GF(P) (with a discontinuity) and Figure 10D shows the same line b' after the module N operation as multiple lines that have the same slope.

As mentioned above, when k is synchronized among transmitters, slightly better performance may be obtained than when there is no synchronization among the transmitters.

Some embodiments synchronize k with the SFN and HSFN. More particularly, assuming deterministic k like this: k₀ = 0, k_t = 1, = N - l, k_N = 0, k_N+1 = 1, ... , the period of the sequences s( j, /c₇) will be N x P. If each channel hop is 320 ms, it means the periodicity is

N x P x 320ms. In NB-loT, one radio frame is 10 ms, and each radio frame is numbered as System Frame Number (SFN) 0, 1 , 1023, in a SFN cycle. A SFN cycle is therefore 10.24 seconds. Each SFN cycle forms a hyper system frame, each of which is labeled with a Hyper

SFN (H-SFN) number, ranging from 0 to 1023. A H-SFN cycle consists of 1024 SFN cycles, i.e.

2²⁰ radio frames. One way to synchronize k and the SFN and H-SFN is to reset the value of k at certain known combination of (SFN, H-SFN). For example, at (SFN, H-SFN)=(0,0), the deterministic value k can be reset as 0. Then, at (SFN, H-SFN)=(x,y), the values of i and j can be computed as i = (1024y+x) (mod 32) and j =(1024y+x) (mod 32*P).

The performance loss of prematurely restarting the period, i.e., in the middle of the sequence set k = 0 and restart, will cause maximally one additional collision. If this is done seldom, the additional performance loss is negligible.

A script where a random parameter k is used for each sequence is shown below. Each row in S1 corresponds to one sequence for a transmitter. By changing k, more sequences for the same transmitters are obtained.

clear;

N = 50;

P = 349;

S1 = [];

% Create a P-1 x P matrix containing P-1 sequences of length P.

for row = 1 :P-1

k = randi([0 N-1]);

S1 (row,:) = mod( mod((0:P-1)*row, P) + k, N);

end

Examples based on the above script and their corresponding performance include the following. As a first example, N = 50, P = 47 and let k be synchronized k. Let s be the set containing 46 FH sequences where each sequence is constructed using k. Then C(5) = ^ =

2.128% for any k. As a second example, N = 50, P = 47 and let k be unsynchronized. Let s be set containing 46 FH sequences where the sequences are constructed in such a way that all available k's are used for at least one sequence. Then C(5) = ^ = 4.255%. As a third example,

.N = 50, P = 349 and let k be synchronized k. Let S_k be the set containing 348 FH sequences where each sequence is constructed using k. Then C(S_k) = ^ = 3.725% for any k. As a fourth example, N = 50, P = 349 and let k be unsynchronized. Let s be a set containing 348 FH sequences where the sequences are constructed in such a way that all available k's are used for at least one sequence. Then C(5) =— = 4.011%.

Finally consider results where P is chosen as prime power (but not power 1 and not power of 2), odd, and even. As a first example, N = 50, P = 49 (49 is a prime power but not power 1 and not power of 2) and let k be synchronized k. Let S_k be the set containing 48 FH sequences where each sequence is constructed using k. Then C(S_k) = -^ = 14.290% for any k.

As a second example, N = 50, P = 45 (odd number) and let k be synchronized k. Let S_k be the set containing 44 FH sequences where each sequence is constructed using k. Then C(5_fe) =

^ = 33.333% for any k. As a third example, N = 50, P = 48 (even number) and let k be synchronized k. Let S_k be the set containing 47 FH sequences where each sequence is constructed using k. Then C(S_k) = ^ = 50% for any k.

Although in various embodiments described above a frequency hopping sequence 18 is based on a sequence constant k, embodiments herein generally include a frequency hopping sequence that may or may not be based on such a sequence constant k. The examples in Figures 10A-10D illustrate this aspect, as none of the lines in those figures are offset from the origin by a sequence constant. Figure 1 1 illustrates processing performed by a radio node in these and other embodiments where a frequency hopping sequence may or may not be based on a sequence constant.

Figure 1 1 illustrates a method 300 implemented by a radio node configured for use in a wireless communication system with N frequencies usable by a frequency hopping pattern. The method 300 includes transmitting or receiving according to a frequency hopping pattern 18 that comprises a frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P (Block 310). The multiple lines each have the same slope. Furthermore, P > N; that is, the length of the frequency sequence and the order of the Galois field is greater than the number of frequencies usable by the frequency hopping pattern. The greater the length P of the frequency sequence compared to the number N of usable frequencies, the more equal the frequency channel usage (on average) over time. Indeed, in the limit of P to infinity, channel usage would be strictly equal. This means that in some embodiments where P > N, basing different frequency hopping patterns used at different times on different sequence constants k may not be needed for equal channel usage.

Regardless of whether or not such a sequence constant is used, though, the method 300 as shown may also include determining (e.g., generating or selecting) the sequence 18 (Block 320). The frequency hopping pattern 18 in some embodiments may otherwise be described in accordance with embodiments above.

In some embodiments, the system 10 according to any of the approaches described above is a NB-loT system. The system in some cases may operate in the unlicensed 902 MHz- 928 MHz band. Figure 12 illustrates one possible channelization in this case, based on a 250 kHz channel separation, having 50 uplink (UL) and 50 downlink (DL) channels. This design would be subject to the regulatory constraints specified in the first row of the table in Figure 1. The number of hopping channels and dwell time constraints imply that the FH patterns for NB- loT should have period 50 and hop over exactly 50 different frequencies, i.e., N=50. The latter requirement is called fairness property herein.

Accordingly, embodiments herein include methods to generate FH patterns for NB-loT systems operating on the 902 MHz-928 MHz band and subject to FCC regulations. The FH patterns generated accordingly to the methods herein have good collision properties and are well suited for frequency hopping spread spectrum NB-loT. That is, the methods minimize the number of collisions for a FH spread-spectrum NB-loT system operating in the 902 MHz-928 MHz band while maximizing the number of those patterns, and subject to the constraints specified in the first row of Figure 1 satisfying the regulations in FCC, for instance the fairness property.

Despite particular applicability to NB-loT in some examples, though, it will be appreciated that the techniques may be applied to other wireless networks, including eMTC as well as to successors of the E-UTRAN. Thus, references herein to signals using terminology from the 3GPP standards for LTE should be understood to apply more generally to signals having similar characteristics and/or purposes, in other networks.

A radio node herein is any type of node (e.g., a base station or wireless communication device) capable of communicating with another node over radio signals. A radio network node 12 is any type of radio node within a wireless communication network, such as a base station. A network node is any type of node within a wireless communication network, whether within a radio access network or a core network of the wireless communication network. A wireless communication device 14 is any type of radio node capable of communicating with a radio network node over radio signals. A wireless communication device 14 may therefore refer to a machine-to-machine (M2M) device, a machine-type communications (MTC) device, a NB-loT device, etc.. The wireless device may also be a UE, however it should be noted that the UE does not necessarily have a "user" in the sense of an individual person owning and/or operating the device. A wireless device may also be referred to as a radio device, a radio communication device, a wireless terminal, or simply a terminal - unless the context indicates otherwise, the use of any of these terms is intended to include device-to-device UEs or devices, machine-type devices or devices capable of machine-to-machine communication, sensors equipped with a wireless device, wireless-enabled table computers, mobile terminals, smart phones, laptop- embedded equipped (LEE), laptop-mounted equipment (LME), USB dongles, wireless customer-premises equipment (CPE), etc. In the discussion herein, the terms machine-to- machine (M2M) device, machine-type communication (MTC) device, wireless sensor, and sensor may also be used. It should be understood that these devices may be UEs, but are generally configured to transmit and/or receive data without direct human interaction.

In an IOT scenario, a wireless communication device 14 as described herein may be, or may be comprised in, a machine or device that performs monitoring or measurements, and transmits the results of such monitoring measurements to another device or a network.

Particular examples of such machines are power meters, industrial machinery, or home or personal appliances, e.g. refrigerators, televisions, personal wearables such as watches etc. In other scenarios, a wireless communication device as described herein may be comprised in a vehicle and may perform monitoring and/or reporting of the vehicle's operational status or other functions associated with the vehicle.

Note that a radio node (e.g., radio network equipment 12 and/or wireless communication device 14, such as a user equipment) as described above may perform the processing herein by implementing any functional means or units. In one embodiment, for example, the radio node comprises respective circuits or circuitry configured to perform the steps shown in Figure 4, 7, 8, 1 1 , and/or in any of the other embodiments. The circuits or circuitry in this regard may comprise circuits dedicated to performing certain functional processing and/or one or more

microprocessors in conjunction with memory. In embodiments that employ memory, which may comprise one or several types of memory such as read-only memory (ROM), random-access memory, cache memory, flash memory devices, optical storage devices, etc., the memory stores program code that, when executed by the one or more processors, carries out the techniques described herein.

Figure 13A illustrates additional details of a radio node 400 (e.g., the radio network node 12 or the wireless communication device 14) in accordance with one or more embodiments. As shown, the radio node 400 includes processing circuitry 410 and radio circuitry 420. The radio circuitry 420 is configured to transmit via one or more antennas 440, which may be internal or external to the radio node 400. The processing circuitry 41 is configured to perform processing described above, e.g., in Figure 4, 7, 8, 1 1 , and/or in any of the other embodiments, such as by executing instructions stored in memory 430. The processing circuitry 410 in this regard may implement certain functional means or units.

Figure 13B illustrates a radio node 450 (e.g., the radio network node 12 or the wireless communication device 14) that according to other embodiments implements various functional means or units, e.g., via the processing circuitry 410 in Figure 13A. As shown, these functional means or units may include for instance a determine module or unit 460 for determining (e.g., generating or selecting) a frequency hopping pattern 18 as described herein. The radio node 450 may also include a transmitting or receiving module or unit 470 for transmitting or receiving according to a frequency hopping pattern 18 as described herein.

Additional details of a wireless communication device 14 in the form of a user equipment are shown in relation to Figure 14. As shown, the example user equipment 14 includes an antenna 540, radio circuitry (e.g. radio front-end circuitry) 510, processing circuitry 520, and the user equipment 14 may also include a memory 530. The memory 530 may be separate from the processing circuitry 520 or an integral part of processing circuitry 520. Antenna 540 may include one or more antennas or antenna arrays, and is configured to send and/or receive wireless signals, and is connected to radio circuitry (e.g. radio front-end circuitry) 510. In certain alternative embodiments, user equipment 14 may not include antenna 540, and antenna5 may instead be separate from user equipment 14 and be connectable to user equipment 14 through an interface or port.

The radio circuitry (e.g. radio front-end circuitry) 510 may comprise various filters and amplifiers, is connected to antenna 540 and processing circuitry 520, and is configured to condition signals communicated between antenna 540 and processing circuitry 520. In certain alternative embodiments, user equipment 14 may not include radio circuitry (e.g. radio front-end circuitry) 510, and processing circuitry 520 may instead be connected to antenna 540 without front-end circuitry 510.

Processing circuitry 520 may include one or more of radio frequency (RF) transceiver circuitry, baseband processing circuitry, and application processing circuitry. In some embodiments, the RF transceiver circuitry 521 , baseband processing circuitry 522, and application processing circuitry 523 may be on separate chipsets. In alternative embodiments, part or all of the baseband processing circuitry 522 and application processing circuitry 523 may be combined into one chipset, and the RF transceiver circuitry 521 may be on a separate chipset. In still alternative embodiments, part or all of the RF transceiver circuitry 521 and baseband processing circuitry 522 may be on the same chipset, and the application processing circuitry 523 may be on a separate chipset. In yet other alternative embodiments, part or all of the RF transceiver circuitry 521 , baseband processing circuitry 522, and application processing circuitry 523 may be combined in the same chipset. Processing circuitry 520 may include, for example, one or more central processing units (CPUs), one or more microprocessors, one or more application specific integrated circuits (ASICs), and/or one or more field programmable gate arrays (FPGAs).

The user equipment 14 may include a power source 550. The power source 550 may be a battery or other power supply circuitry, as well as power management circuitry. The power supply circuitry may receive power from an external source. A battery, other power supply circuitry, and/or power management circuitry are connected to radio circuitry (e.g. radio front- end circuitry) 510, processing circuitry 520, and/or memory 530. The power source 550, battery, power supply circuitry, and/or power management circuitry are configured to supply user equipment 14, including processing circuitry 520, with power for performing the functionality described herein.

Additional details of the radio network node 12 are shown in relation to Figure 15. As shown, the example radio network node 12 includes an antenna 640, radio circuitry (e.g. radio front-end circuitry) 610, processing circuitry 620, and the radio network node 12 may also include a memory 630. The memory 630 may be separate from the processing circuitry 620 or an integral part of processing circuitry 620. Antenna 640 may include one or more antennas or antenna arrays, and is configured to send and/or receive wireless signals, and is connected to radio circuitry (e.g. radio front-end circuitry) 610. In certain alternative embodiments, radio network node 12 may not include antenna 640, and antenna 640 may instead be separate from radio network node 12 and be connectable to radio network node 12 through an interface or port.

The radio circuitry (e.g. radio front-end circuitry) 610 may comprise various filters and amplifiers, is connected to antenna 640 and processing circuitry 620, and is configured to condition signals communicated between antenna 640 and processing circuitry 620. In certain alternative embodiments, radio network node 12 may not include radio circuitry (e.g. radio front- end circuitry) 610, and processing circuitry 620 may instead be connected to antenna 640 without front-end circuitry 610.

Processing circuitry 620 may include one or more of radio frequency (RF) transceiver circuitry, baseband processing circuitry, and application processing circuitry. In some embodiments, the RF transceiver circuitry 621 , baseband processing circuitry 622, and application processing circuitry 623 may be on separate chipsets. In alternative embodiments, part or all of the baseband processing circuitry 622 and application processing circuitry 623 may be combined into one chipset, and the RF transceiver circuitry 621 may be on a separate chipset. In still alternative embodiments, part or all of the RF transceiver circuitry 621 and baseband processing circuitry 622 may be on the same chipset, and the application processing circuitry 623 may be on a separate chipset. In yet other alternative embodiments, part or all of the RF transceiver circuitry 621 , baseband processing circuitry 622, and application processing circuitry 623 may be combined in the same chipset. Processing circuitry 620 may include, for example, one or more central processing units (CPUs), one or more microprocessors, one or more application specific integrated circuits (ASICs), and/or one or more field programmable gate arrays (FPGAs).

The radio network node 12 may include a power source 650. The power source 650 may be a battery or other power supply circuitry, as well as power management circuitry. The power supply circuitry may receive power from an external source. A battery, other power supply circuitry, and/or power management circuitry are connected to radio circuitry (e.g. radio front- end circuitry) 610, processing circuitry 620, and/or memory 630. The power source 650, battery, power supply circuitry, and/or power management circuitry are configured to supply radio network node 12, including processing circuitry 620, with power for performing the functionality described herein.

Those skilled in the art will also appreciate that embodiments herein further include corresponding computer programs.

A computer program comprises instructions which, when executed on at least one processor of a radio node 400, 450, cause the radio node 400, 450 to carry out any of the respective processing described above. A computer program in this regard may comprise one or more code modules corresponding to the means or units described above.

Embodiments further include a carrier containing such a computer program. This carrier may comprise one of an electronic signal, optical signal, radio signal, or computer readable storage medium.

In this regard, embodiments herein also include a computer program product stored on a non-transitory computer readable (storage or recording) medium and comprising instructions that, when executed by a processor of a (transmitting or receiving) radio node 400, 450, cause the radio node 400, 450 to perform as described above.

Embodiments further include a computer program product comprising program code portions for performing the steps of any of the embodiments herein when the computer program product is executed by a computing device. This computer program product may be stored on a computer readable recording medium.

In view of the above, some embodiments are capable of generating arbitrary sets of FH sequences. Any FH sequence in any two sets has good collision properties between one another.

Further in this regard, some embodiments include a method, implemented in a radio node i in a frequency hopping spread spectrum wireless system, to determine a FH pattern from a total of P - 1 patterns, using N channels, and tune the center of frequency of the transceiver based on said FH pattern. The method comprises (a) Determining the sequence index p (b) Generating a first number sequence depending on the number ? and _έ. (c) Determining a sequence constant k. (d) Generating a second number sequence by adding the constant k to each entry in the first number sequence. And (e) Generating a FH sequence by limiting the numbers in the second number sequence such that the largest number is T — l.

In some embodiments, p is a prime.

In some embodiments, p is a power prime.

In some embodiments, p is an odd number.

In some embodiments, b) further comprises generating a line in a finite affine plane over the finite field with p elements.

In some embodiments, c) further comprises letting k be fixed for each generated FH pattern for transmitter i. In some embodiments, c) further comprises letting k change deterministically for each generated FH pattern.

In some embodiments, c) further comprises letting k change randomly for each generated FH pattern.

In any of the above embodiments, determining a sequence constant k may further comprise synchronization of k among all radio nodes i.

Embodiments include a method to generate arbitrarily many FH sequences with good properties. The method works well for composite number of channels available.

Embodiments further include a method implemented by a radio node configured for use in a wireless communication system. The method comprises determining a sequence constant. The method further comprises determining a frequency hopping pattern based on the sequence constant, wherein the frequency hopping pattern comprises a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P , wherein the one or more lines each have the same slope and wherein at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant. The method also comprises transmitting or receiving according to the frequency hopping pattern.

In some embodiments, the method comprises determining the sequence constant as a function of a system frame number and/or a hyper system frame number in which the radio node is to transmit or receive according to the frequency hopping pattern, wherein a hyper system frame comprises multiple system frame numbers.

In some embodiments, the method comprises determining the sequence constant to be the same as a sequence constant based on which another radio node determines a frequency hopping pattern according to which the another radio node is to transmit or receive.

In some embodiments, the method comprises determining the sequence constant by determining, from a set of sequentially ordered sequence constants, a next sequence constant that is sequentially ordered after a previous sequence constant based on which the radio node previously determined a frequency hopping pattern.

In some embodiments, the method comprises determining the sequence constant by randomly or pseudo-randomly determining the sequence constant from a set of multiple sequence constants.

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the N frequencies are indexed from an initial index to the initial index plus N , and wherein the sequence constant has a value that is greater than or equal to the initial index and that is less than or equal to the initial index plus N .

In some embodiments, the method further comprises determining a sequence slope parameter, and determining the frequency hopping pattern also based on the sequence slope parameter, wherein the one or more lines each have a slope equal to the sequence slope parameter. In some embodiments, the sequence slope parameter is specific for the radio node. In some embodiments, the method further comprises receiving signaling indicating assignment of the sequence slope parameter to the radio node. In some embodiments, the sequence slope parameter is one of multiple different possible sequence slope parameters associated with different possible frequency hopping sequences.

In some embodiments, the slope is greater than or equal to 1 and is less than or equal to

P - l .

In some embodiments, the one or more lines are a single line.

k, [( - 1) x p] + k} in the Galois field GF(P), where k is the sequence constant and p is the slope.

In some embodiments, the one or more lines comprise multiple lines.

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, and wherein P > N .

In some embodiments, the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the frequency indices in the frequency sequence each have a value less than N .

In some embodiments, wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the frequency hopping pattern comprises a frequency sequence sip, k) of length P with frequency indices corresponding to sip, k) =

{v₀imod Ν),

= {(0 x p) +

k, (1 x p) + k, (2 x p) + k, ... , [iP - 1) x p] + k] in the Galois field GF(P), where k is the sequence constant and p is the slope.

In some embodiments, P is prime. In some embodiments, P is a prime power. In some embodiments, P is an odd number.

In some embodiments, the method comprises determining the frequency hopping pattern comprises generating the frequency hopping pattern based on the sequence constant. In some embodiments, determining the frequency hopping pattern comprises selecting the frequency hopping pattern from a set or table of frequency hopping patterns based on the sequence constant.

In some embodiments, the method further comprises: determining a different sequence constant; determining a different frequency hopping pattern based on the different sequence constant, wherein the different frequency hopping pattern comprises a different frequency sequence of length P with frequency indices from one or more different lines in a finite affine plane over a Galois field with an order equal to P , wherein the one or more different lines each have said same slope and wherein at least one of the one or different more lines is offset from the origin of the Galois field by the different sequence constant; and switching from transmitting or receiving according to the frequency hopping pattern to transmitting or receiving according to the different frequency hopping pattern.

In some embodiments, the wireless communication system is a narrowband internet of things system.

Embodiments also include a method implemented by a radio node configured for use in a wireless communication system with N frequencies usable by a frequency hopping pattern. The method comprises transmitting or receiving according to a frequency hopping pattern that comprises a frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P , wherein the multiple lines each have the same slope and wherein P > N .

In some embodiments, the method further comprises determining a sequence constant and determining the frequency hopping pattern based on the sequence constant, wherein at least one of the multiple lines is offset from the origin of the Galois field by the sequence constant.

In some embodiments, the method comprises determining the sequence constant by randomly or pseudo-randomly determining the sequence constant from a set of multiple sequence constants. In some embodiments, the N frequencies are indexed from an initial index to the initial index plus N , and wherein the sequence constant has a value that is greater than or equal to the initial index and that is less than or equal to the initial index plus N .

In some embodiments, the method further comprises determining a sequence slope parameter, and determining the frequency hopping pattern based on the sequence slope parameter, wherein the multiple lines each have a slope equal to the sequence slope parameter. In some embodiments, the sequence slope parameter is specific for the radio node. In some embodiments, the method further comprises receiving signaling indicating assignment of the sequence slope parameter to the radio node. In some embodiments, the sequence slope parameter is one of multiple different possible sequence slope parameters associated with different possible frequency hopping sequences. In some embodiments, the slope is greater than or equal to 1 and is less than or equal to P - \ .

In some embodiments, the frequency indices in the frequency sequence each have a value less than N .

In some embodiments, the frequency hopping pattern comprises a frequency sequence of length P with frequency indices corresponding to {[(0 x p) + k]mod N, [(1 x p) +

k]mod N, [(2 x p) + k]mod N, ... , [[(P - 1) x p] + k]mod N} in the Galois field GF(P), where k is a sequence constant and p is the slope.

{v₀imod Ν),

= {(0 x p) +

In some embodiments, N is a composite number.

In some embodiments, determining the frequency hopping pattern comprises generating the frequency hopping pattern.

In some embodiments, determining the frequency hopping pattern comprises selecting the frequency hopping pattern from a set or table of frequency hopping patterns.

For example, embodiments include a radio node configured for use in a wireless communication system. The radio node is configured to: determine a sequence constant; determine a frequency hopping pattern based on the sequence constant, wherein the frequency hopping pattern comprises a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P , wherein the one or more lines each have the same slope and wherein at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant; and transmit or receive according to the frequency hopping pattern.

The radio node in some embodiments is configured to perform the method of any of the above embodiments.

Embodiments also include a radio node configured for use in a wireless communication system. The radio node comprises a constant determining module for determining a sequence constant; a pattern determining module for determining a frequency hopping pattern based on the sequence constant, wherein the frequency hopping pattern comprises a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P , wherein the one or more lines each have the same slope and wherein at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant; and a transmitting or receiving module for transmitting or receiving according to the frequency hopping pattern.

In some embodiments, the radio node comprises one or more modules for performing the method of any of the above embodiments.

Embodiments further include a radio node configured for use in a wireless

communication system. The radio node comprises radio circuitry and processing circuitry wherein the radio node is configured to: determine a sequence constant; determine a frequency hopping pattern based on the sequence constant, wherein the frequency hopping pattern comprises a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P , wherein the one or more lines each have the same slope and wherein at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant; and transmit or receive according to the frequency hopping pattern.

In some embodiments, the radio node comprises radio circuitry and processing circuitry wherein the radio node is configured to perform the method of any of the above embodiments.

Embodiments also include a radio node configured for use in a wireless communication system with N frequencies usable by a frequency hopping pattern. The radio node is configured to transmit or receive according to a frequency hopping pattern that comprises a frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P , wherein the multiple lines each have the same slope and wherein P > N .

In some embodiments, the radio node is configured to perform the method of any of the above embodiments. Embodiments also include a radio node configured for use in a wireless communication system. The radio node comprises a transmitting or receiving module for transmitting or receiving according to a frequency hopping pattern that comprises a frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P , wherein the multiple lines each have the same slope and wherein P > N .

Embodiments also include a radio node configured for use in a wireless communication system. The radio node comprises radio circuitry and processing circuitry wherein the radio node is configured to transmit or receive according to a frequency hopping pattern that comprises a frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P , wherein the multiple lines each have the same slope and wherein P > N .

Embodiments also include a computer program comprising instructions which, when executed by at least one processor of a radio node, causes the radio node to carry out the method of any of the above embodiments. Embodiments also include a carrier containing such a computer program, wherein the carrier is one of an electronic signal, optical signal, radio signal, or computer readable storage medium.

Embodiments also include a method implemented by a radio node configured for use in a wireless communication system that has a number N of frequency channels. The method comprises: generating a shifted number sequence by shifting each number in a number sequence by a sequence constant; generating a frequency hopping sequence from the shifted number sequence, by, for any number in the shifted number sequence greater than N-1 , reducing the number to be less than or equal to N-1 ; and transmitting or receiving a signal according to the generated frequency hopping sequence.

The present invention may, of course, be carried out in other ways than those specifically set forth herein without departing from essential characteristics of the invention. The present embodiments are to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.

Claims

CLAIMS What is claimed is:

1. A method implemented by a radio node (12, 14, 400, 450) configured for use in a wireless communication system, the method comprising:

determining (120) a frequency hopping pattern (18) based on a sequence constant, wherein the frequency hopping pattern (18) comprises a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P , wherein the one or more lines each have the same slope and wherein at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant; and transmitting or receiving (130) according to the frequency hopping pattern (18).

2. The method of claim 1 , wherein the wireless communication system has N frequencies usable by a frequency hopping pattern (18), and wherein P < N .

3. A method implemented by a radio node (12, 14, 400, 450) configured for use in a wireless communication system with N frequencies usable by a frequency hopping pattern (18), the method comprising:

transmitting or receiving (310) according to a frequency hopping pattern (18) that

comprises a frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P , wherein the multiple lines each have the same slope and wherein P > N .

4. The method of claim 3, wherein at least one of the multiple lines is offset from the origin of the Galois field by a sequence constant.

5. The method of any of claims 1-2 and 4, wherein the sequence constant is a function of a system frame number and/or a hyper system frame number in which the radio node (12, 14, 400, 450) is to transmit or receive according to the frequency hopping pattern (18), wherein a hyper system frame comprises multiple system frame numbers.

6. The method of any of claims 1-2 and 4-5, wherein the sequence constant is the same as a sequence constant on which is based another frequency hopping pattern according to which another radio node is to transmit or receive.

7. The method of any of claims 1-2 and 4-6, wherein the sequence constant is included in a set of sequentially ordered sequence constants and is sequentially ordered after a previous sequence constant on which is based a frequency hopping pattern according to which the radio node (12, 14, 400, 450) previously transmitted or received.

8. The method of any of claims 1-2 and 4-7, wherein the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein the N frequencies are indexed from an initial index to the initial index plus N , and wherein the sequence constant has a value that is greater than or equal to the initial index and that is less than or equal to the initial index plus N .

9. The method of any of claims 1-8, further comprising determining a sequence slope parameter, and determining the frequency hopping pattern (18) based on the sequence slope parameter, wherein the one or more lines each have a slope equal to the sequence slope parameter.

10. The method of claim 9, further comprising receiving signaling indicating assignment of the sequence slope parameter to the radio node (12, 14, 400, 450).

1 1. The method of any of claims 1-2 and 5-10, wherein the wireless communication system has N frequencies usable by a frequency hopping pattern (18), wherein P < N , and wherein the frequency hopping pattern (18) comprises a frequency sequence of length P with frequency indices corresponding to {(0 x p) + k, (1 x p) + k, (2 x p) + k, [(P - 1) x p] + k} in the Galois field GF(P), where k is the sequence constant and p is the slope.

12. The method of any of claims 1-2 and 4-10, wherein the wireless communication system has N frequencies usable by a frequency hopping pattern (18), wherein the frequency hopping pattern (18) comprises a frequency sequence sip, k) of length P with frequency indices corresponding to sip, k) = {v₀imod N),

N)}, where vector s =

{v₀, v_t, ... vp-i) = {(0 x p) + k, (1 x p) + k, (2 x p) + k, ... , [(P - 1) x p] + k} in the Galois field GF(P), where k is the sequence constant and p is the slope.

13. The method of any of claims 1-12, wherein P is prime.

14. The method of any of claims 1-13, wherein the wireless communication system has N frequencies usable by a frequency hopping pattern, wherein N is a composite number.

15. The method of any of claims 1-14, further comprising: determining a different frequency hopping pattern based on a different sequence constant, wherein the different frequency hopping pattern comprises a different frequency sequence of length P with frequency indices from one or more different lines in a finite affine plane over a Galois field with an order equal to P , wherein the one or more different lines each have said same slope and wherein at least one of the one or different more lines is offset from the origin of the Galois field by a different sequence constant; and

switching from transmitting or receiving according to the frequency hopping pattern (18) to transmitting or receiving according to the different frequency hopping pattern.

16. The method of any of claims 1-15, wherein the wireless communication system is a narrowband internet of things system, and wherein transmitting or receiving according to the frequency hopping pattern (18) is performed in an unlicensed frequency band.

17. A radio node (12, 14, 400, 450) configured for use in a wireless communication system, the radio node (12, 14, 400, 450) configured to:

determine a frequency hopping pattern (18) based on a sequence constant, wherein the frequency hopping pattern (18) comprises a frequency sequence of length P with frequency indices from one or more lines in a finite affine plane over a Galois field with an order equal to P , wherein the one or more lines each have the same slope and wherein at least one of the one or more lines is offset from the origin of the Galois field by the sequence constant; and

transmit or receive according to the frequency hopping pattern (18).

18. The radio node of claim 17, configured to perform the method of any of claims 2 and 5- 16.

19. A radio node (12, 14, 400, 450) configured for use in a wireless communication system with N frequencies usable by a frequency hopping pattern, the radio node (12, 14, 400, 450) configured to:

transmit or receive according to a frequency hopping pattern (18) that comprises a

frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P , wherein the multiple lines each have the same slope and wherein P > N .

20. The radio node of claim 19, configured to perform the method of any of claims 4-16.

21. A radio node (12, 14, 400) configured for use in a wireless communication system, the radio node (12, 14, 400) comprising radio circuitry (420) and processing circuitry (410) wherein the radio node (12, 14, 400) is configured to:

transmit or receive according to the frequency hopping pattern (18).

22. The radio node of claim 21 , comprising radio circuitry (420) and processing circuitry (410) wherein the radio node (12, 14, 400, 450) is configured to perform the method of any of claims 2 and 5-16.

23. A radio node (12, 14, 400) configured for use in a wireless communication system, the radio node (12, 14, 400) comprising radio circuitry (420) and processing circuitry (410) wherein the radio node (12, 14, 400) is configured to:

transmit or receive according to a frequency hopping pattern (18) that comprises a frequency sequence of length P with frequency indices from multiple lines in a finite affine plane over a Galois field with an order equal to P , wherein the multiple lines each have the same slope and wherein P > N .

24. The radio node of claim 23, comprising radio circuitry (420) and processing circuitry (410) wherein the radio node (12, 14, 400, 450) is configured to perform the method of any of claims 5-16.

25. A computer program comprising instructions which, when executed by at least one processor of a radio node (12, 14, 400, 450), causes the radio node (12, 14, 400, 450) to carry out the method of any of claims 1-16.

26. A carrier containing the computer program of claim 25, wherein the carrier is one of an electronic signal, optical signal, radio signal, or computer readable storage medium.