RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent Application Serial Number 62/465,123 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 particularly 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 Bluetooth and GSM. 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, 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. 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. In some embodiments, the frequency hopping pattern comprises multiple partial frequency hopping patterns concatenated together. In other embodiments, the frequency hopping pattern comprises a Reed Solomon code based frequency hopping pattern

concatenated with an orderly frequency sequence. Regardless, the frequency hopping pattern according to some embodiments may be usable even in a wireless communication system that necessitates that the pattern have a certain length and/or period that is non-prime. For example, the wireless communication system herein may be a NB-loT system, e.g., operating on the 902 MHz-928 MHz band and subject to FCC regulations.

More particularly, embodiments herein include a method implemented by a radio node configured for use in a wireless communication system. The method comprises transmitting or receiving a signal according to a frequency hopping pattern that comprises first and second partial frequency hopping patterns concatenated together. In some embodiments, the first and second partial frequency hopping patterns have respective first and second lengths that are prime numbers. The sum of these prime numbers in one embodiment is equal to a period and/or length of the frequency hopping pattern.

In some embodiments, each frequency index in the first partial frequency hopping pattern has a value that is less than or equal to an initial index plus the first length minus one, and each frequency index in the second partial frequency hopping pattern has a value that is greater than or equal to the initial index plus the first length..

Alternatively or additionally, in some embodiments, each frequency index in the first partial frequency hopping pattern has a value that is greater than or equal to an initial index and less than or equal to the initial index plus the first length minus one, and each frequency index in the second partial frequency hopping pattern has a value that is greater than or equal to the initial index plus the first length and less than or equal to the initial index plus the first length plus the second length minus one.

In some embodiments, the period of the frequency hopping pattern and/or a length of the frequency hopping period is a composite number. Alternatively or additionally, the period of the frequency hopping pattern and/or a length of the frequency hopping period may not be a prime power, wherein a prime power is a power of a prime number.

In some embodiments, frequency indices in the first partial frequency hopping pattern form a line in a finite affine plane over a first Galois field, wherein the first Galois field has an order equal to the first length. Alternatively or additionally, frequency indices in the second partial frequency hopping pattern, as each reduced by the first length, form a line in a finite affine plane over a second Galois field, wherein the second Galois field has an order equal to the second length.

In some embodiments, the method further comprises generating the frequency hopping pattern by generating a first line in a finite affine plane over a first Galois field, wherein the first Galois field has an order equal to the first length, and generating a second line in a finite affine plane over a second Galois field, wherein the second Galois field has an order equal to the second length. Generation may further comprise shifting the second line by adding the first length to each point on the second line, and concatenating the first line and the shifted second line.

In some embodiments, the first partial frequency hopping pattern is a pattern

a _n (k) = n - k(mod p) , for k = 0, ...,p -\ , where p is the first length and 1 < n < p -\ .

Alternatively or additionally, the second partial frequency hopping pattern is a pattern b _n \k) = n - k(mod q) + p , for k = 0,...,q - \ , where q is the second length, where 1 < n < p -l , and where p is the first length.

In some embodiments, the first partial frequency hopping pattern is a pattern

a _n (k) = n - k(mod p) , for k = 0, ...,p -\ , wherein the second partial frequency hopping pattern is a pattern b _n \k) = n - k(mod q) + p , for k = 0,...,q -\ , where p is the first length, where q is the second length, and 1 < n < p -l , and wherein the frequency hopping pattern is a pattern c _n = {a _n (0), a _n (1), ...a _n (p - 1), b _n '(0), b _n '(1), .. b _n \q - 1)} .

In some embodiments, the method further comprises determining the frequency hopping pattern, from amongst a set of candidate frequency hopping patterns. Each candidate frequency hopping pattern in the set comprises respective first and second partial frequency hopping patterns concatenated together. The respective first and second partial frequency hopping patterns have the first and second lengths. In one embodiment, for example, the candidate frequency hopping patterns in the set comprise

c _B « _B (0 i), ...« -i ⁾ A m 0^ _^

a _n (k) = n - k(mod p) , for k = 0, ...,p -\ and for n = \,...,p -\ , and where

b _n \k) = n - k(mod q) + p , for k = 0,...,q -\ and for n = \,...,p -\ , where p is the first length and where q is the second length.

Embodiments also include a radio node configured for use in a wireless communication system. The radio node is configured to transmit or receive a signal according to a frequency hopping pattern that comprises first and second partial frequency hopping patterns

concatenated together, wherein the first and second partial frequency hopping patterns have respective first and second lengths that are prime numbers whose sum is equal to a period of the frequency hopping pattern.

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. Further included may be a carrier containing the 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. The method comprises transmitting or receiving a signal according to a frequency hopping pattern that comprises a Reed Solomon code based frequency hopping pattern concatenated with an orderly frequency sequence.

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

In some embodiments, the Reed Solomon code based frequency hopping pattern is generated or generatable based on the Reed Solomon code RS(q -\,\, q -\) over the Galois field GF{q) , where q is a prime power. In some embodiments, q is the largest prime power less than a period of the frequency hopping pattern.

In some embodiments, the Reed Solomon code based frequency hopping pattern has a length equal to q -l and includes each frequency, except for one missing frequency, in the set of frequencies {f ₀ , f ₁ , f ₂ , _~ -f _q - ₁ }■ In one embodiment, the orderly frequency sequence includes the one missing frequency. In one embodiment, the orderly frequency sequence includes at least one frequency outside the set.

In some embodiments, the period of the frequency hopping pattern is a composite number and is not a prime power, wherein a prime power is a power of a prime number.

In some embodiments, the method further comprises determining the frequency hopping pattern, from amongst a set of candidate frequency hopping patterns. Each candidate frequency hopping pattern in the set comprises a Reed Solomon code based frequency hopping pattern concatenated with an orderly frequency sequence.

Embodiment also include a radio node configured for use in a wireless communication system. The radio node is configured to transmit or receive a signal according to a frequency hopping pattern that comprises a Reed Solomon code based frequency hopping pattern concatenated with an orderly frequency sequence.

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. Further included may be a carrier containing the computer program, wherein the carrier is one of an electronic signal, optical signal, radio signal, or computer readable storage medium. Frequency hopping patterns generated or used according to some embodiments herein have good collision properties and are well suited for frequency hopping spread spectrum systems such as NB-loT. 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 3 is a logic flow diagram of a method performed by a radio node according to some embodiments.

Figure 4 is a block diagram of a frequency hopping pattern according to some embodiments.

Figure 5A is a diagram representing a first partial frequency hopping sequence as a line in a finite affine plane over a Galois field according to some embodiments.

Figure 5B is a diagram representing a second partial frequency hopping sequence as a line in a finite affine plane over a Galois field according to some embodiments.

Figure 5C is a diagram representing a shifted version of the second partial frequency hopping sequence as a shifted line in a finite affine plane over a Galois field according to some embodiments.

Figure 5D is a diagram representing a frequency hopping sequence formed from concatenating the first and second partial sequences according to some embodiments.

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

Figure 6B is a logic flow diagram of an algorithm for generating a frequency hopping pattern according to some embodiments.

Figure 7 is a table showing a set of frequency hopping patterns according to some embodiments.

Figure 8 is a logic flow diagram of a method performed by a radio node according to other embodiments.

Figure 9 is a logic flow diagram of an algorithm for generating a set of frequency hopping patterns according to some embodiments.

Figures 10A-10B are a table showing a set of frequency hopping patterns according to other embodiments.

Figure 11 is a logic flow diagram of an algorithm for generating a set of frequency hopping patterns 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 1 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.

According to some embodiments, the frequency hopping pattern 18 comprises multiple partial frequency hopping patterns concatenated together or comprises a Reed Solomon code based frequency hopping pattern concatenated with an orderly frequency sequence. In either case such concatenation may for instance yield a frequency hopping pattern 18 that is usable even in a wireless communication system 10 with constraints that necessitate that the pattern 18 have a certain length and/or period which is a composite number (e.g., not a prime and not a prime power). For example, the wireless communication system 10 may even be a NB-loT system, e.g., operating on the 902 MHz-928 MHz band and subject to FCC regulations.

In more detail, Figure 3 illustrates a method 100 implemented by a radio node (e.g., radio network node 12 or wireless communication device 14) configured for use in a wireless communication system 10 according to some embodiments. The method 100 as shown comprises transmitting or receiving a signal 16 according to a frequency hopping pattern 18 that comprises first and second partial frequency hopping patterns concatenated together (Block 1 10). The first and second partial frequency hopping patterns have respective first and second lengths that are prime numbers whose sum is equal to a period of (and/or a length of) the frequency hopping pattern 18. In some embodiments, for example, the sum of the first and second lengths may be a composite number (e.g., 50). Alternatively or additionally, the sum of the first and second lengths may not be a prime power (i.e., a power of a prime number). In any event, the method 100 in some embodiments further comprises determining such a frequency hopping pattern 18 (Block 120), such as by generating the pattern 18 or selecting the pattern 18 (e.g., from a table of patterns).

Figure 4 illustrates one example of a frequency hopping pattern 18 that has a period and/or length of N=50. As shown, the frequency hopping pattern 18 in Figure 4 is comprised of first and second partial frequency hopping patterns 18A and 18B, respectively. The first partial frequency hopping pattern 18A has a first length p that is equal to the prime number 19 and the second partial frequency hopping pattern 18B has a second length q that is equal to the prime number 31. The sum of p and q is equal to N=50, i.e., the period and/or length of the pattern 18.

In some embodiments, the frequency indices in the first and second partial frequency hopping patterns 18A, 18B are disjoint or mutually exclusive of one another. Figure 4 in this regard shows that the frequency indices in the first partial frequency hopping pattern 18A each have a value that is less than or equal to p-1 (i.e., less than or equal to 18 in this example), whereas the frequency indices in the second partial frequency hopping pattern 18B each have a value that is greater than or equal to p (i.e..greater than or equal to 19 in this example) . In fact, Figure 4 shows that the frequency indices in the first partial frequency hopping pattern 18A each have a value that is greater than or equal to zero and that is less than or equal to p-1 , whereas the frequency indices in the second partial frequency hopping pattern 18A each have a value that is greater than or equal to p and that is less than or equal to p+q-1. The particular frequency indices in Figure 4's example are non-limiting, as other embodiments include other sequences of such indices.

This of course assumes that the frequency indices start with an index of 0. Generally, for any value of the initial index, each frequency index in the first partial frequency hopping pattern 18A has a value that is less than or equal to an initial index (e.g., 0) plus the first length p minus one, and each frequency index in the second partial frequency hopping pattern 18B has a value that is greater than or equal to the initial index plus the first length p. Or more specifically, each frequency index in the first partial frequency hopping pattern 18A may have a value that is greater than or equal to an initial index and less than or equal to the initial index plus the first length p minus one, and each frequency index in the second partial frequency hopping pattern 18B may have a value that is greater than or equal to the initial index plus the first length p and less than or equal to the initial index plus the first length p plus the second length q minus one.

In at least some embodiments, the frequency hopping pattern 18 may correspond to these frequency indices due at least in part to the way in which the frequency hopping pattern 18 is structured. In some embodiments, for example, frequency indices in the first partial frequency hopping pattern 18A form (e.g., are from) a line in a finite affine plane over a first Galois field GF(p), i.e., the first Galois field has an order equal to the first length 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. Alternatively or additionally, frequency indices in the second partial frequency hopping pattern 18B, as each reduced by the first length p, form (e.g., are from) a line in a finite affine plane over a second Galois field GF(q), i.e., the second Galois field has an order equal to the second length q.

Figures 5A-5D illustrate additional details of this structure according to some

embodiments, from the perspective of how this structure is generated, e.g., by the radio node or some other node. As shown in Figure 5A, generation of the frequency hopping pattern 18 involves generating a first line a _n (k) = n ^■ k(mod p) for k = 0, ...,p -\ in a finite affine plane over a first Galois field GF{p) , where p is the first length of the first partial frequency hopping sequence 18A and \ < n < p -l . Here, n effectively defines the slope of this first line. As shown, n = 2 . The dotted line in Figure 5A illustrates that the sequence in fact produces a single line in a finite affine plane over the Galois field. a _n (k) may also be referred to as a vector, with its elements coming from the Galois field GF{p) , which 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 is equivalent to a line in a finite affine plane over GF{p) .

Also, as shown in Figure 5B, generation of the frequency hopping pattern 18 further involves generating a second line b _n (k) = n ^■ k(mod q) , for k = 0,...,q -l in a finite affine plane over a second Galois field GF(q) , where q is the second length of the second partial frequency hopping sequence 18B, where 1 < n < p -l , and where p is the first length. The dotted line in Figure 5B similarly illustrates that the sequence in fact produces a single line in a finite affine plane over the Galois field.

As shown in Figure 5C, generation next entails shifting the second line b _n by adding the first length p to each point on the second line b _n , resulting in a shifted second line b _n ' , where b _n \k) = n - k(mod q) + p . Figure 5D shows that the first line a _n and the shifted second line b _n ' are concatenated together, to thereby generate the frequency hopping sequence 18 in the form of c _n = A ' } = { _¾ (0), a _n (1), ...a _n (p - 1), b _n '(0), b _n '(1), .. b _n \q - 1)} .

Note that different frequency hopping patterns may be formed by using different values for n above, e.g., so that the line(s) associated with the patterns have different slopes. Patterns formed in this way may have desirable collision properties. In this sense, then, a set of frequency hopping patterns (with desirable collision properties) may include patterns formed with different values of n . In some embodiments, the radio node that transmits or receives according to such frequency hopping sequence 18 actually generates that sequence 18, e.g., as described above. In other embodiments, the radio node selects a frequency hopping sequence 18 that has previously been generated by another node (e.g., offline). Such selection may be from a set of multiple frequency hopping sequences (e.g., in a look-up table) with similar structure. Either way, the frequency hopping sequence 18 according to which the radio node transmits or receives may be structured as described above.

In more detail, suppose that the system 10 hops over N different frequencies

{fo, fi, f2 ... , jv-i}- These frequencies are the centers of frequency of the N available hopping radio frequency channels. The exact value of the frequencies N is irrelevant for the purpose of designing frequency hopping (FH) patterns, and any set of N different elements suffices to label the different frequencies. Hence, without loss of generality, as used herein the set of frequencies will be labeled {0,1,2, ... , N - 1}, with the implicit understanding that the label k corresponds to the frequency f _k . An FH pattern is just a sequence of frequencies with a given period. It follows that only the elements within one period need to be specified. Given two FH patterns a and b with period N

a = {α(0), α(2), ... , a(N - 1)},

ή = {ή(0), ή(1) b(N - 1)},

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

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

The expression H(a, b) 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 N = 4, and let

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

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

The calculation of H(a, b) is visualized with the help of the table in Figure 6A. 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 6A:

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

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

EQ 1) H(C) = max{H(a, b)}.

a.bes One or more embodiments herein include methods to construct sets C of FH patterns having a small H(C). An integer that is not a prime number is called a composite number. Given a positive integer s, it is challenging to find sets C of FH patterns satisfying the following properties: (1) The number of frequencies N used in each FH pattern is composite, and not the power of a prime; (2) The period of any FH pattern in C is exactly N; (3) Any FH pattern in C contains exactly N different frequencies (the fairness property); (4) The figure of merit H(C) of the set C is less than or equal to K; and (5) One frequency should appear in all the patterns.

For example, N = 50 satisfies condition 1 above. Conditions 2 and 3 mean that a(n)≠ a(m) whenever n≠ m. Some embodiments herein address the design of sets of FH patterns satisfying conditions 1-5.

In a "first embodiment", consider the case where the number N of different frequencies used in each FH pattern is composite, and not the power of a prime. Let p and q be prime numbers such that p + q = N. Without loss of generality, assume p < q. Define a set A of sequences a _n , n = Ι, .,. , ρ - 1, by:

EQ 2) a _n (Jt) = n ^■ k (mod p), k = 0, ... , p— 1

H(A) = 1. Similarly, define a set s of sequences b _n , n = Ι, .,. , ρ - 1, by

EQ 3) b _n (k) = n - k (mod q), k = 0, ... , q— 1,

which also has the property that H(B) = 1. Both sets of FH patterns have p - 1 elements. A function of a real variable x defined by f(x) = n ^■ x is just a line with slope n. Similarly, a _n is a line with slope n belonging to a so-called finite affine plane in a finite affine geometry over the Galois field GF(p). By the same token, b _n is a line with slope n belonging to a finite affine plane in a finite affine geometry over the Galois field GF(q) . More generally, one could generate the set B by taking any p - 1 of the q - 1 lines b _n , 1≤ n≤ q - 1.

A set C of FH patterns hopping over N frequencies is generated from A and B as follows. For n = 1, ... , p - 1, the set includes the sequences:

EQ 4) c _n = {a _n (0), a _n (l), ... , a _n (p - 1), b _n (0) + p, b _n (l) + p, ... , b _n (q - 1) + p}.

An arbitrary FH pattern c in the set C may be generated as follows and as illustrated in Figure 6B. In the shown method 130, after determining a period N of the FH pattern to be generated (Step 140), prime numbers p and q are determined such that p + q = N (Step 150). Then, a first line in the finite affine plane over GF(p) is generated (Step 160). This line contains exactly p different elements, with numerical values between 0 and p - 1. Analogously, a second line in the finite affine plane over GF(q) is generated (Step 170). This line contains exactly q different elements, with numerical values between, and including, 0 and q - 1. Then, the second line is shifted by adding the number p to each of the elements in the line (Step 180). Thus, a shift by p is implemented by adding the number p to all the elements in the line, which are themselves integers. Hence, the shift operation results in numerical values between, and including, p and N - 1. In particular, none of these values coincides with a value taken by the elements in the first line, since the latter are all strictly less than p. Fourth, the first line and the shifted second line are concatenated, yielding an FH pattern of period N containing exactly N different elements (Step 190).

The steps 160-190 are repeated, each time choosing lines not previously used, in order to generate new FH patterns. Up to p - 1 different FH patterns can be generated by means of this procedure. The set C of FH patterns thus generated inherits good collision properties of the parent sets A and B, as quantified by the figure of merit H(C).

The first embodiment may be illustrated by means of an example with N = 50. The integers p, q are not unique. They may be chosen such that a) p + q = N; b) Both p, q are primes, p≤ q; and c) |p - q \ is as small as possible. This is to maximize the number of lines in the set A, and consequently the number of FH patterns p in the set C.

The choices p = 19 and q = 31 satisfy the requirements a) to c). Straightforward application of EQ 2), EQ 3) and EQ 4) results in the set C containing 18 different FH patterns, shown as Table 3 in Figure 7. Each column in the table contains one FH pattern and the table header #n is a label for the n-th FH pattern c _n . Numerical evaluation of the figure of merit according to EQ1 yields H(C) = 2.

Accordingly, some embodiments herein include a method implemented by a radio node configured for use in a wireless communication system. The method comprises selecting a frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns, or cyclically shifted versions thereof, in Table 3. That is, all or a portion of the patterns in Table 3 may be the patterns from which the radio node selects, either exactly as shown in Table 3 or as cyclically shifted. In any event, the method further comprises transmitting or receiving a signal according to the selected frequency hopping pattern.

Other embodiments herein include a method, implemented in a radio node in a frequency hopping spread spectrum wireless system, to determine a FH pattern of period N and tune the center of frequency of the transceiver based on said FH pattern. The method may comprise determining prime numbers p and q such their sum is equal to the period N of the FH pattern. The method may further comprise generating a first partial FH pattern depending on the prime p and generating a second partial FH pattern depending on the prime q. The method may further entail shifting the second partial FH pattern by the amount p, and concatenating the first partial FH pattern and the shifted second partial FH pattern. In some embodiments, the method may further comprise transmitting or receiving a signal according to the resulting frequency hopping pattern.

In some embodiments, generating a first partial FH pattern further comprises generating a line in a finite affine plane over the finite field with p elements, and generating a second FH pattern further comprises generating a line in a finite affine plane over the finite field with q elements. Alternatively or additionally, the integers p and q may be chosen such that the magnitude of their difference is as small as possible

Alternatively or additionally, N may be a composite number.

Figure 8 shows a method implemented by a radio node configured for use in a wireless communication system 10 according to still other embodiments. As shown, the method 200 comprises transmitting or receiving a signal 16 according to a frequency hopping pattern 18 that comprises a Reed Solomon code based frequency hopping pattern concatenated with an orderly frequency sequence (Block 210). The Reed Solomon code based frequency hopping pattern may be for instance a frequency hopping pattern that is generated or generatable using a Reed Solomon code In some embodiments, for example, the Reed Solomon code based frequency hopping pattern is generated or generatable based on the Reed Solomon code RS(q -\,\, q -\) over the Galois field GF{q) , where q is a prime power. In one embodiment, q is the largest prime power less than a period of the frequency hopping pattern. In any event, the method may also comprise determining (e.g., generating or selecting) the sequence 18 (Block 220).

In some embodiments, these embodiments may create 49 FH patterns, compared to 18 FH patterns described above, at the expense of slightly increasing the collision number to 3.

In more detail, consider the Galois Field GF(q) with the order q where q is a power of prime number p. Then, a set C of the sequences of length n = q - 1 with number of collisions H(C) = K can be constructed utilizing the error-correcting Reed-Solomon code RS(n, K, n— K +

!) ^■

For the case K = 1, the construction of sequences in C may allow counting the number of sequences in C. These sequences satisfy the fairness property (each is using exactly q alphabets from GF(q)). Let e ₀ and e ₁ be the basis vectors of the constructed sequence set C by RS(n, l, n) and a be an arbitrary chosen element from GF(q). Then, the sequences of C, where for the purpose of counting the collisions the cyclic shifts are excluded, looks like a ^■ e ₀ + e _t . Therefore, there exist q sequences of the length n = q - 1 with H(C) = 1 in C due to the q different possibilities for the choice of a from GF(q).

Based on the construction of RS(n, 1, n), the FH patterns over N = n + 2 different frequencies {/o _< /i _< /2 - N-I} with figure of merit H(C) = 3 is illustrated as follows and in the method of Figure 9. After determining q as the larget prime power smaller than the period N of the FH patterns to be generated (Step 310), the error-correcting code RS(n, l, n) is used to build set C _a containing q = n + 1 patterns of the length n = q - 1 (Step 320). Each pattern a _{ in C _a for j = 0, ... , n - 1 lacks one frequency f _t from the set of frequencies {f ₀ , f _t , f ₂ ... , f _n }. Additionally, based on construction, patterns c^'s collide in at most 1 place since K = 1. Next, the method includes constructing the set of FH patterns C _b where each pattern b for i = 0, ... , n - 1, is of the length n + 1 by adding the corresponding missing frequency f _t at the end of each pattern a _{ (Step 330). Such FH patterns bi's collide in at most 2 places and therefore H(C) = 2 for C _b . Then, the method includes adding the frequency f _N at the end of each b _t (Step 340). This allows construction of the final set C _f of the n new patterns with the length N and maximum 3 collisions (Step 350). This implies H(C) = 3 for C _f . These steps generate a FH pattern set C _f containing q = n + 1 patterns inheriting the fairness property from RS(n, 1, n) and satisfying the good collision properties with a figure of merit H( cf) = 3.

Some embodiments are illustrated by means of an example with the period N = 50 using construction of Reed-Solomon code. Set q = 7 ² and n = q - 1 = 48 to generate 49 FH patterns, the set C _a , using RS(48,1,48) with H(C _a ) = 1. Positioning the corresponding missing frequency at the end of the pattern of C _a leads to the set C _b containing 49 FH patterns of the length 49 with fairness property and H(C _b ) = 2. Finally, the favorable FH pattern set C _f constructed using the frequencies {/o _< /i _< /2 - _> g] with ^H { ^c r) = 3 is introduced by considering the frequency ₄₉ at the end of all patterns in C _b .

Table 4 in Figures 10A-10B illustrates an example of set C _f of FH patterns of period N = 50 and having a figure of merit {c ) = 3. Each column in the table contains one FH patterns and the table header #i is a label for the i-th FH pattern c _t .

In view of the above, some embodiments includes a method, implemented in a radio node in a frequency hopping spread spectrum wireless system, to determine a FH pattern of period N from the frequency set {/o _< /i _< /2 - _N - _I } ^an d ^tune the center of frequency of the transceiver based on said FH pattern. The method may comprise determining the largest prime power q < N. The method may also comprise generating the code, containing q sequences, using RS(q - 1,1, q - 1) over GF(q). The method may further comprise adding orderly sequence of frequencies f _q , f _q+1 - ,† _N - _I at the end of each sequence. In some embodiments, N is a composite number.

Other embodiments herein include a computer aided design method, to determine a FH pattern of period N from the frequency set / = {/o _< /i _< /2 - _N - _I } based on improving the random permutations by upward shifts in the frequencies. The method may comprise generating M number of FH patterns by randomly permuting elements in f; Constructing a set of new patterns by considering adding the numbers 0: N - 1 (mod N) to the labels of the M patterns; and Repeating this construction for many times and saving the M permutations with the least number of collisions in the set. In some embodiments, N is a composite number.

In more detail, some embodiments construct the FH patterns satisfying a fairness property based on a computer aided design with the objective of providing a good H(C) for a certain number of frequency channels. Let N be the composite number of hopping channels that transmitters are hopping over. Then, the algorithm according to some embodiments is as follows and as shown in Figure 11. After determining the number N of frequency channels (Step 410), the algorithm includes generating M random permutations from the frequencies

{fo,fi,f ₂ - ,†N-I (Step 420). The permutations include:

a _± = {<¾(()), - (..), ... , a _± (N - 1)},

a ₂ = { ₂ (0), α ₂ (1), ... , a ₂ QV - 1)},...

a _M = {a _M (0), a _M (l), ... , a _M (N - 1)}.

Next, the algorithm in Steps 430-460 includes constructing a set C containing M ^■ N number of FH patterns c _{m n} , for all n = 0, ... , N - 1, of permutations a _m where m = Ι, .,. , Μ as follows:

For n = 0, ... , N - 1, c _{m n} (i) = (a _m ( + n) (mod N), i = 0, ... , N - 1.

The algorithm involves iterating these steps a number of times and saving the parent sequences a _t , a ₂ , ... , _M leading to the lowest H(C) (Step 470).

This leads to the set C of M ^■ N FH patterns of the length N with the minimum figure of merit H(C). An advantage with this algorithm is using a rather modest memory requirement (in total M ^■ N + 1 bytes of the integers). In addition, such construction has a very low complexity, see step 440 for fixed n. And finally, this methodology is extendable to a larger number of the patterns by choosing a large M. Applying the introduced computer aided design to the case of N = 50 where M = 2, a set of 100 FH patterns C, with H(C) = 5, may be created.

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 3, 6, 8, 9, 11 , and/or any of the enumerated 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 500 (e.g., radio network node 12 or wireless communication device 14) in accordance with one or more embodiments. As shown, the radio node 500 includes processing circuitry 510 and radio circuitry 520. The radio circuitry 520 is configured to transmit via one or more antennas 540, which may be internal or external to the radio node. The processing circuitry 510 is configured to perform processing described above, e.g., in Figure 3, 6B, 8, 9, 1 1 , and/or any of the enumerated embodiments, such as by executing instructions stored in memory 530. The processing circuitry 510 in this regard may implement certain functional means or units.

Figure 13B illustrates a radio node 550 (e.g., radio network node 12 or wireless communication device 14) that according to other embodiments implements various functional means or units, e.g., via the processing circuitry 510 in Figure 13A. As shown, these functional means or units may include for instance a determine module or unit 560 for determining (e.g., generating or selecting) a frequency hopping pattern 18 as described herein. The radio node 550 may also include a transmitting or receiving module or unit 570 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 640, radio circuitry (e.g. radio front-end circuitry) 610, processing circuitry 620, and the user equipment 14 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, user equipment 14 may not include antenna 640, and antenna 640 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) 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 940 and processing circuitry 620. In certain alternative embodiments, user equipment 14 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 user equipment 14 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 user equipment 14, including processing circuitry 620, 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 740, radio circuitry (e.g. radio front-end circuitry) 710, processing circuitry 720, and the radio network node 12 may also include a memory 730. The memory 730 may be separate from the processing circuitry 720 or an integral part of processing circuitry 720. Antenna 740 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) 710. In certain alternative embodiments, radio network node 12 may not include antenna 740, and antenna 740 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) 710 may comprise various filters and amplifiers, is connected to antenna 740 and processing circuitry 720, and is configured to condition signals communicated between antenna 740 and processing circuitry 720. In certain alternative embodiments, radio network node 12 may not include radio circuitry (e.g. radio front- end circuitry) 710, and processing circuitry 720 may instead be connected to antenna 740 without front-end circuitry 710.

Processing circuitry 720 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 721 , baseband processing circuitry 722, and application processing circuitry 723 may be on separate chipsets. In alternative embodiments, part or all of the baseband processing circuitry 722 and application processing circuitry 723 may be combined into one chipset, and the RF transceiver circuitry 721 may be on a separate chipset. In still alternative embodiments, part or all of the RF transceiver circuitry 721 and baseband processing circuitry 722 may be on the same chipset, and the application processing circuitry 723 may be on a separate chipset. In yet other alternative embodiments, part or all of the RF transceiver circuitry 721 , baseband processing circuitry 722, and application processing circuitry 723 may be combined in the same chipset. Processing circuitry 720 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 750. The power source 750 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) 710, processing circuitry 720, and/or memory 730. The power source 750, battery, power supply circuitry, and/or power management circuitry are configured to supply radio network node 12, including processing circuitry 720, 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 500, 550, cause the radio node 500, 550 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 500, 550, cause the radio node 500, 550 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 variations and modifications, embodiments herein generally include a method implemented by a radio node configured for use in a wireless communication system. The method comprises transmitting or receiving a signal according to a frequency hopping pattern that comprises first and second partial frequency hopping patterns concatenated together. The first and second partial frequency hopping patterns have respective first and second lengths that are prime numbers whose sum is equal to a period of the frequency hopping pattern.

In some embodiments, the first and second partial frequency hopping patterns each comprise a frequency sequence in which frequencies in the sequence have a respective index. Each frequency index in the first partial frequency hopping pattern has a value that is less than or equal to an initial index plus the first length minus one, and each frequency index in the second partial frequency hopping pattern has a value that is greater than or equal to the initial index plus the first length.

Alternatively or additionally, in some embodiments the first and second partial frequency hopping patterns each comprise a frequency sequence in which frequencies in the sequence have a respective index. Each frequency index in the first partial frequency hopping pattern has a value that is greater than or equal to an initial index and less than or equal to the initial index plus the first length minus one, and each frequency index in the second partial frequency hopping pattern has a value that is greater than or equal to the initial index plus the first length and less than or equal to the initial index plus the first length plus the second length minus one.

In some embodiments, the period of the frequency hopping pattern and/or a length of the frequency hopping period is a composite number.

In some embodiments ,the period of the frequency hopping pattern and/or a length of the frequency hopping period is not a prime power, wherein a prime power is a power of a prime number.

In some embodiments, the frequency hopping pattern contains a number of frequency indices that is equal to the period of the frequency hopping pattern.

In some embodiments, the first length is less than the second length.

In some embodiments, the first length is equal to the second length.

In some embodiments, frequency indices in the first partial frequency hopping pattern form a line in a finite affine plane over a first Galois field, wherein the first Galois field has an order equal to the first length. In some embodiments, frequency indices in the second partial frequency hopping pattern, as each reduced by the first length, form a line in a finite affine plane over a second Galois field, wherein the second Galois field has an order equal to the second length.

In some embodiments, the method further comprises generating or selecting the frequency hopping pattern.

In some embodiments, the method further comprises generating the frequency hopping pattern by: generating a first line in a finite affine plane over a first Galois field, wherein the first Galois field has an order equal to the first length; generating a second line in a finite affine plane over a second Galois field, wherein the second Galois field has an order equal to the second length; shifting the second line by adding the first length to each point on the second line; and concatenating the first line and the shifted second line.

In some embodiments, the first partial frequency hopping pattern is a pattern

a _n (k) = n - k(mod p) , for k = 0, ...,p -\ , where p is the first length and \ < n < p -\ . In some embodiments, the second partial frequency hopping pattern is a pattern

b _n \k) = n - k(mod q) + p , for k = 0,...,q - \ , where q is the second length, where 1 < n < p -l , and where p is the first length.

In some embodiments, the first partial frequency hopping pattern is a pattern

a _n (k) = n - k(mod p) , for k = 0, ...,p -\ , wherein the second partial frequency hopping pattern is a pattern b _n \k) = n - k(mod q) + p , for k = 0,...,q -\ , where p is the first length, where q is the second length, and 1 < n < p -l , and wherein the frequency hopping pattern is a pattern c _n = {a _n (0), a _n (1), ...a _n (p - 1), b _n '(0), b _n '(1), .. b _n \q - 1)} .

In some embodiments, the period of the frequency hopping pattern is equal to 50.

In some embodiments, a difference between the first length and the second length is less than 15. In some embodiments, the first length is equal to 19 and the second length is equal to 31.

In some embodiments, the method further comprises determining the frequency hopping pattern, from amongst a set of candidate frequency hopping patterns. Each candidate frequency hopping pattern in the set comprises respective first and second partial frequency hopping patterns concatenated together. The respective first and second partial frequency hopping patterns have the first and second lengths. In some embodiments, each frequency index in the respective first partial frequency hopping pattern has a value that is greater than or equal to an initial index and less than or equal to the initial index plus the first length minus one, and each frequency index in the respective second partial frequency hopping pattern has a value that is greater than or equal to the initial index plus the first length and less than or equal to the initial index plus the first length plus the second length minus one. In some embodiments, the number of candidate frequency hopping patterns in the set is equal to the first length minus one. In some embodiments, the candidate frequency hopping patterns in the set are formed from respective first partial frequency hopping patterns a _n (k) = n - k(mod p) , for k = 0, ...,p -\ and for n = \,...,p -\ , where p is the first length. In some embodiments, the candidate frequency hopping patterns in the set are formed from respective second partial frequency hopping patterns b _n \k) = n - k(mod q) + p , for k = 0,...,q -\ and for n = \,...,p -\ , where p is the first length and where q is the second length. In some embodiments, the candidate frequency hopping patterns in the set comprise c _n = {a _n {0 a _n {\ ...a _n {p - \\ b _n '(0), b„ '(l),...b„ \q - \)} for « = !,..., ? -! , where a _n (k) = n - k(mod p) , for k = 0, ...,p -\ and for n = \,...,p -1 , and where b _n \k) = n - k(mod q) + p , for k = 0,...,q -\ and for n = \,...,p -\ , where p is the first length and where q is the second length.

In some embodiments, the frequency hopping pattern is one of, or is a cyclically shifted version of one of, the frequency hopping patterns in Table 3 of Figure 7.

In some embodiments, the method further comprises selecting the frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Table 3 of Figure 7, or cyclically shifted versions thereof.

Embodiments also include a method implemented by a radio node configured for use in a wireless communication system. The method comprises selecting a frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Table 3 of Figure 7, or cyclically shifted versions thereof. The method also comprises transmitting or receiving a signal according to the selected frequency hopping pattern.

Embodiments further include a method implemented by a radio node configured for use in a wireless communication system. The method comprises generating a frequency hopping pattern c _n = {a _n (0), a _n (1), .. a _n (p - 1), b _n (0) + p, b _n (1) + p, .. b _n (q - 1) + p) where

a _n (k) = n - k(mod p) , for k = 0, ...,p -\ , where b _n (k) = n - k(mod q) , for k = 0,...,q - \ , and where 1 < n < p -\ . The method also comprises transmitting or receiving a signal according to the generated frequency hopping pattern.

In some embodiments, ^ and q are each prime numbers, and wherein p + q is a composite number that is not a prime power, wherein a prime power is a power of a prime number.

Embodiment also include a method implemented by a radio node configured for use in a wireless communication system. The method comprises generating a first partial frequency hopping pattern as a function of a first prime number, and generating a second partial frequency hopping pattern as a function of a second prime number. The method further comprises shifting the second partial frequency hopping pattern by the first prime number. The method further comprises forming a frequency hopping pattern by concatenating the first partial frequency hopping pattern and the shifted second partial frequency hopping pattern. The method also comprises transmitting or receiving a signal according to the formed frequency hopping pattern.

In some embodiments, at least one of: generating the first partial frequency hopping pattern comprises generating the first partial frequency hopping pattern as a first line in a finite affine plane over a first Galois field, wherein the first Galois field has an order equal to the first prime number, and wherein generating the second partial frequency hopping pattern comprises generating the second partial frequency hopping pattern as a second line in a finite affine plane over a second Galois field, wherein the second Galois field has an order equal to the second prime number. In some embodiments, the sum of the first prime number and the second prime number is a composite number that is not a prime power.

Embodiments also include aradio node configured for use in a wireless communication system. The radio node is configured to transmit or receive a signal according to a frequency hopping pattern that comprises first and second partial frequency hopping patterns

concatenated together, wherein the first and second partial frequency hopping patterns have respective first and second lengths that are prime numbers whose sum is equal to a period of the frequency hopping pattern.

In some embodiments, the radio node is configured to perform the method of any of the above embodiments.

Embodiments furher 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 a signal according to a frequency hopping pattern that comprises first and second partial frequency hopping patterns concatenated together, wherein the first and second partial frequency hopping patterns have respective first and second lengths that are prime numbers whose sum is equal to a period of the frequency hopping pattern.

In some embodiments, the radio node further comprises one or more modules for performing 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 comprising radio circuitry and processing circuitry wherein the radio node is configured to transmit or receive a signal according to a frequency hopping pattern that comprises first and second partial frequency hopping patterns concatenated together, wherein the first and second partial frequency hopping patterns have respective first and second lengths that are prime numbers whose sum is equal to a period of 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 further include a radio node configured for use in a wireless

communication system. The radio node is configured to select a frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Table 3 of Figure 7, or cyclically shifted versions thereof. The radio node is also configured to transmit or receive a signal according to the selected frequency hopping pattern.

Embodiments also include a radio node configured for use in a wireless communication system. The radio node comprises a selecting module for selecting a frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Table 3 of Figure 7, or cyclically shifted versions thereof. The radio node also comprises a transmitting or receiving module for transmitting or receiving a signal according to the selected frequency hopping pattern. 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 select a frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Table 3 of Figure 7, or cyclically shifted versions thereof, and to transmit or receive a signal according to the selected frequency hopping pattern.

Embodiments also include a radio node configured for use in a wireless communication system. The radio node is configured to generate a frequency hopping pattern

c„ = (°X ^a „ OX · · - ^a „ (P - !), *„ (0) + P, K (1) + p,...b _n {q - \) + p) where a _n (k) = n - £(mod ?) , for k = 0, ...,p -\ , where b _n (k) = n ^■ k(mod q) , for k = 0,...,q -\ , and where \ < n < p -\ . The radio node is also configured to transmit or receive a signal according to the generated frequency hopping pattern.

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 generating module for generating a frequency hopping pattern c _n = {a _n (0), a _n (1), .. a _n (p - 1), b _n (0) + p, b _n (1) + p, .. b _n (q - 1) + p) where

a _n (k) = n - k(mod p) , for k = 0, ...,p -\ , where b _n (k) = n - k(mod q) , for k = 0,...,q - \ , and where 1 < n < p -\ . The radio node also includes a transmitting or receiving module for transmitting or receiving a signal according to the generated frequency hopping pattern.

In some embodiments, the radio node is configured to perform 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 comprising radio circuitry and processing circuitry wherein the radio node is configured to generate a frequency hopping pattern

cn = n (°X ^a n O · · ¾ (p ^~ I), ( ⁰ ) + P, K (1) + p, .. \ (q - 1) + _P ) where ¾ (k) = π · k(mod ?) , for k = 0, ...,p -\ , where b _n (k) = n ^■ k(mod q) , for k = 0,...,q -\ , and where \ < n < p -l , and to transmit or receive a signal according to the generated frequency hopping pattern.

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 is configured to generate a first partial frequency hopping pattern as a function of a first prime number, and generate a second partial frequency hopping pattern as a function of a second prime number. The radio node is also configured to shift the second partial frequency hopping pattern by the first prime number. The radio node is further configured to form a frequency hopping pattern by concatenating the first partial frequency hopping pattern and the shifted second partial frequency hopping pattern, and transmit or receive a signal according to the formed frequency hopping pattern.

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 first generating module for generating a first partial frequency hopping pattern as a function of a first prime number, and a second generating module for generating a second partial frequency hopping pattern as a function of a second prime number. The radio node further comprsies a shifting module for shifting the second partial frequency hopping pattern by the first prime number, and a forming module for forming a frequency hopping pattern by concatenating the first partial frequency hopping pattern and the shifted second partial frequency hopping pattern. The radio node also include a transmitting or receiving module for transmitting or receiving a signal according to the formed frequency hopping pattern.

In some embodiments, the radio 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 radio circuitry and processing circuitry wherein the radio node is configured to generate a first partial frequency hopping pattern as a function of a first prime number; generate a second partial frequency hopping pattern as a function of a second prime number; shift the second partial frequency hopping pattern by the first prime number; form a frequency hopping pattern by concatenating the first partial frequency hopping pattern and the shifted second partial frequency hopping pattern; and transmit or receive a signal according to the formed frequency hopping pattern.

In some embodiments, the radio node is configured to perform the method of any of the above embodiments.

Embodiments further 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 additionally include a method implemented by a radio node configured for use in a wireless communication system. The method comprises transmitting or receiving a signal according to a frequency hopping pattern that comprises a Reed Solomon code based frequency hopping pattern concatenated with an orderly frequency sequence. In some embodiments, the Reed Solomon code based frequency hopping pattern is generated or generatable based on the Reed Solomon code RS(q -\,\, q -\) over the Galois field GF{q) , where q is a prime power.

In some embodiments, q is the largest prime power less than a period of the frequency hopping pattern.

In some embodiments, the Reed Solomon code based frequency hopping pattern has a length equal to q -l and includes each frequency, except for one missing frequency, in the set of frequencies {f _Q , f^} .

In some embodiments, the orderly frequency sequence includes the one missing frequency.

In some embodiments, the orderly frequency sequence includes at least one frequency outside the set.

In some embodiments, the period of the frequency hopping pattern is a composite number.

In some embodiments, the period of the frequency hopping pattern is not a prime power, wherein a prime power is a power of a prime number.

In some embodiments, the frequency hopping pattern contains a number of frequencies that is equal to the period of the frequency hopping pattern.

In some embodiments, the method further comprises generating or selecting the frequency hopping pattern.

In some embodiments, the period of the frequency hopping pattern is equal to 50.

In some embodiments, the frequency hopping pattern is one of the frequency hopping patterns in Figures 10A-10B, or a cyclically shifted version thereof.

In some embodiments, the method further comprises determining the frequency hopping pattern, from amongst a set of candidate frequency hopping patterns. Each candidate frequency hopping pattern in the set comprises a Reed Solomon code based frequency hopping pattern concatenated.

In some embodiments, the method further comprises selecting the frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Figures 10A and 10B, or cyclically shifted versions thereof.

Embodiments also include a method implemented by a radio node configured for use in a wireless communication system. The method comprises selecting a frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Figures 10A- 10B, or cyclically shifted versions thereof, and transmitting or receiving a signal according to the selected frequency hopping pattern.

Embodiments also include a radio node configured for use in a wireless communication system. The radio node is configured to transmit or receive a signal according to a frequency hopping pattern that comprises a Reed Solomon code based frequency hopping pattern concatenated with an orderly frequency sequence.

In some embodiments, the radio node is configured to perform 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 a transmitting or receiving module for transmitting or receiving a signal according to a frequency hopping pattern that comprises a Reed Solomon code based frequency hopping pattern concatenated with an orderly frequency sequence.

In some embodiments, the radio node comprises one or more modules for performing the method of any of 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 transmit or receive a signal according to a frequency hopping pattern that comprises a Reed Solomon code based frequency hopping pattern concatenated with an orderly frequency sequence.

In some embodiments, the radio node is configured to perform the method of any of the above embodiments.

Embodiments additionally include a radio node configured for use in a wireless communication system. The radio node is configured to select a frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Figures 10A and 10B, or cyclically shifted versions thereof, and to transmit or receive a signal according to the selected frequency hopping pattern.

Embodiments also include a radio node configured for use in a wireless communication system. The radio node comprises a selecting module for selecting a frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Figures 10A and 10B, or cyclically shifted versions thereof. The radio node further comprises a transmitting or receiving module for transmitting or receiving a signal according to the selected frequency hopping pattern.

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 select a frequency hopping pattern from amongst two or more of the candidate frequency hopping patterns in Figures 10A and 10B, or cyclically shifted versions thereof, and to transmit or receive a signal according to the selected frequency hopping pattern.

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.

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.