GB2571277A

GB2571277A - Method for fine timing synchronisation

Info

Publication number: GB2571277A
Application number: GB1802822.5A
Authority: GB
Inventors: Ornstein Mecklenburg Kasper; Berg Axel; Troha Douglas
Original assignee: ARM Ltd; Advanced Risc Machines Ltd
Current assignee: ARM Ltd
Priority date: 2018-02-21
Filing date: 2018-02-21
Publication date: 2019-08-28
Anticipated expiration: 2038-02-21
Also published as: GB2571277B; GB201802822D0

Abstract

There is described a method of determining the base station timing offset of a received NB-IoT (Narrowband Internet of Things) signal comprising a Narrowband Primary Synchronisation Signal (NPSS), the NPSS having a known, predetermined sequence of symbols. The method includes storing a set of accumulation values S4, the accumulation values in the set comprise terms derived from samples taken from the signal at timings corresponding to the predetermined sequence of symbols. The method further includes determining a cross-correlation between the set of accumulation values and a portion of the predetermined sequence of symbols S5; and determining, from the cross-correlation, which of a set of candidate timing offsets corresponds to the timing offset of the received signal S6. The method may determine the fine timing once the UE has determined the course timing estimation to a precision of at least plus or minus half a symbol in devices which may be low-cost or lower power NB-IoT devices with limited computational resources. Determining accumulation values in hardware circuitry may allow the central processing unit of the device to be used for other purposes while the accumulation values are being determined.

Description

METHOD FOR FINE TIMING SYNCHRONISATION

Technical Field

The present relates to the field of Narrowband Internet of Things (NB-IoT), a 3GPP standard designed for low power and low bit rate devices. More particular, the disclosure relates to a method for determining the base station timing of an NB-IoT signal using a Narrowband Primary Synchronization Signal (NPSS).

Background

NB-IoT is the fifth-generation of mobile communication technologies standard developed within the 3rd Generation Partnership Project, 3GPP. One of the purposes is to improve the Universal Mobile Telecommunication System (UMTS) standard to cope with future requirements in terms of improved services such as improved efficiency and lowered costs. In a typical UMT system, wireless devices or terminals also known as mobile stations and/or user equipment units (UEs) communicate via a radio access network (RAN) to one or more core networks.

When a UE, such as a wireless communication device, is powered on it will attempt to connect to a network. The process of attempting to connect to a network includes a frequency band scan, time/frequency synchronisation, and a cell search. There are pre-determined frequencies bands in which the UE will perform the frequency band scan and while performing the frequency band scan the UE will look for a Narrowband Primary Synchronization Signal (NPSS), which has a known pattern. The UE uses the NPSS to perform timing synchronisation and to estimate the frequency offset. In one implementation, the UE performs timing synchronisation by first applying an autocorrelation method to determine a coarse timing estimation, then applying cross-correlation to determine the fine timing.

Cross-correlation, as used to determine the fine timing, is computationally expensive in terms of the number of operations performed and in terms of the number of registers required to perform the computations.

Summary

According to a first aspect, there is provided a method of determining a timing offset of a received signal containing a Narrowband Primary Synchronisation Signal (NPSS), the NPSS having a predetermined sequence of symbols. The method includes storing a set of accumulation values, an accumulation value in the set comprising an accumulation of terms, terms in the accumulation of terms being derived from samples taken from the received signal at timings corresponding to the predetermined sequence of symbols. The method further includes determining a cross-correlation between the set of accumulation values and data corresponding to a portion of the predetermined sequence of symbols, and then determining, from the cross-correlation, which of a set of candidate timing offsets corresponds to the timing offset of the received signal.

Determining a timing offset of a received signal by storing a set of accumulation values and then determining a cross-correlation using the set of accumulation values can provide a significant saving in terms of computational cost and memory requirements. Such savings are particularly important for NB-IoT devices, which may be low-cost and/or low-power devices and may have very limited computational resources.

According to a second aspect, there is provided a device operable to determine a timing offset of a received signal containing a Narrowband Primary Synchronisation Signal (NPSS), the NPSS having a predetermined sequence of symbols. The device includes a memory configured to store a set of accumulation values, an accumulation value in the set comprising an accumulation of terms, terms in the accumulation of terms being derived from samples taken from the received signal at timings corresponding to the predetermined sequence of symbols. The device further includes processing circuitry configured to determining a cross-correlation between the set of accumulation values and data corresponding to a portion of the predetermined sequence of symbols, and then to determine, from the cross-correlation, which of a set of candidate timing offsets corresponds to the timing offset of the received signal.

According to an example, the processing circuitry of a device is configured to derive each term within a set of accumulation values from a sample taken from a received signal, and to accumulate the derived terms, whereby to determine the accumulation value.

According to an example, a device includes hardware circuitry configured to derive each term within a set of accumulation values from a sample taken from a received signal, and to accumulate the derived terms, whereby to determine the accumulation value. Determining accumulation values in hardware circuitry allows the central processing unit of the device to be used for other purposes while the accumulation values are being determined.

Further features and advantages of the invention will become apparent from the following description of preferred embodiments of the invention, given by way of example only, which is made with reference to the accompanying drawings.

Brief Description of the Drawings

Figure 1 shows 40ms of a Narrowband Internet of Things (NB-IoT) signal.

Figure 2 is a flowchart illustrating a method of processing a received signal.

Figure 3a shows a cover code used within the definition of an NPSS sequence.

Figure 3b shows a cross-correlation mask used for detecting the presence of an NPSS in a received signal.

Figure 4 is a flowchart illustrating a method for detecting the presence of, and coarse timing estimate for, an NPSS in a received signal.

Figure 5 shows a processed signal in the time domain.

Figure 6 is a flowchart illustrating a method for determining a timing offset for a received signal containing an NPSS.

Figure 7 illustrates three symbols of an NPSS sequence.

Figure 8 schematically shows a subframe of an NPSS sequence.

Figure 9 is a flowchart illustrating a method for determining an accumulation value.

Figure 10 is a plot showing the probability of determining a correct timing offset of a received signal.

Fig 11 is a block diagram representing an example of a user equipment (UE) unit.

Detailed Description

Figure 1 shows 40ms of NB-IoT data including the NPSS. The NPSS sequence is located in subframe 5 and its periodicity is 10ms, allowing a UE to accumulate an NPSS in a received signal multiple times over windows of 10ms in order to lower the Signal to Noise Ratio (SNR). The NB-IoT data further includes the signal Narrowband Physical Broadcast Channel (NPBCH), the Physical Downlink Shared Channel (PDSCH), and the Narrowband Secondary Synchronization Signal (NSSS-1) among others. Figure 1 shows a resource map for an example of in-band deployment, where the NPSS occupies the last 11 orthogonal frequency division multiplex (OFDM) symbols of subframe 5 and is punctured by a Long Term Evolution Cell-Specific Reference signal (LTE CRS).

The NPSS is chosen to have good correlation properties, and in the case of NBIoT, is defined in the frequency domain in terms of a Zadoff-Chu sequence of length 11, root sequence index 5, and a cover code S, as shown in Equation (1):

di(n) = S(Z) · exp

Snn(n + 1)\ ~^j---ΪΓ~ )' (1) where n = 0,1,..., 10 labels the lowest 11 subcarriers in the NB-IoT physical resource block (PRB), and Z = 0,1,..., 13 labels the 14 OFDM symbols in subframe 5. The cover code S is given by Equation (2):

= [0,0,0,1,1,1,1, -1, -1,1,1,1, -1,1], (2)

The sequence of Equation (1) is transformed into the time domain before being transmitted.

An exemplary method will now be described in which a user equipment unit (UE) detects a Narrowband Primary Synchronisation Signal (NPSS) within a received signal and determines a coarse timing estimation using the NPSS. As shown in Figure 2, the method begins by receiving, at step SO, a streamed or saved signal within a frequency band. In this example, the streamed or saved signal is a Narrowband Internet of Things (NB-IoT) signal.

The method proceeds by processing, at SI, the received signal. Processing the received signal in this example includes performing, at Sil, low-pass filtration of the received signal to reduce the effect of wideband noise. Processing the received signal in this example further comprises decimating the received signal at S12. In this example, the received signal is sampled at a rate of 1.92MHz, and the signal is decimated by a factor of 8, resulting in 240kHz data. In other examples, decimation is not performed, resulting in improved robustness at low SNR.

Processing the received signal further comprises performing, at S13, partial autocorrelation of the signal using a partial autocorrelation algorithm, and performing, at S14, cross-correlation of the partially autocorrelated signal using a cross-correlation algorithm and a cross-correlation mask. The partial autocorrelation function a(m) is defined by Equation (3):

n-m (3) where *i = x(ri), x₂ = conj (x(n + M_symbol)),

M_Symboi is the number of samples per symbol, and x(n) is the time domain data of the received signal within the frequency band. In this example, the summation in Equation (3) is performed recursively as shown by Equation (4) below:

«(⁰)= Σ^Χ1(^Π)*^Χ2Η «(1) = α(θ) - x_t (θ) * x₂ (θ) + x₇ (μ^_ο1 ) * x₂ (M_symbol), (4)

(m -1 + M_symboI) * x₂ (m -1 + M_symboI).

The cross-correlation function p(m) is defined by Equation (5):

m+HM_symb01-l ρ(ηί) = n-m where in this example the cross-correlation mask s(n) is defined in terms of the cover code S by Equation (6):

s(n) = S(n) · S(n + 1). (6)

The cover code S and the cross-correlation mask s are shown in Figures 3a and 3b respectively. The cross-correlation mask is chosen such that the magnitude of output of the cross-correlation function p(m) is high when the cross-correlation mask matches well with the partially-autocorrelated signal.

The processed signal is accumulated, at S2, over multiple time periods having a predetermined duration. In this example, accumulating comprises saving the processed signal to a memory. In this example, the predetermined duration is equal to the periodicity of the NPSS. According to the NB-IoT standard, the periodicity of the NPSSis 10ms.

The presence of an NPSS is detected, at S3, and if the presence of an NPSS is detected, the coarse timing of the detected NPSS is determined. As shown in Figure 4, an exemplary method for detecting, at S31, the presence of an NPSS comprises determining, at S301, a T-statistic value from the processed signal data accumulated at

S2. In this example, determining the T-statistic value comprises calculating a ratio of the magnitude of the processed signal at the highest peak tpl to the magnitude of the processed signal at the second highest peak tp2. Figure 5 shows an example of processed signal for 10ms of accumulated processed signal data. Here the highest peak, tpl, has a magnitude of around 5.1 and the second highest, tp2, has a magnitude value of around 1.7. This gives a T-statistic value of around 3.

The T-statistic value is analysed at S302. The data x is determined to contain an NPSS only if the T-statistic value is above a certain threshold. In the example of Figure 10, an NPSS is present.

In the case that the data x of the received signal is determined to contain an NPSS, the time corresponding to the highest peak tpl is noted. The time corresponding to the highest peak tpl is then used to determine, at S32, a coarse timing estimate for the received signal. The time corresponding to the highest peak tpl corresponds approximately to the time at which the NPSS is located in the measured data. Since the NPSS is known to be in a specific subframe (in this example, subframe 5), the coarse timing estimate can be determined. In the example of Figure 5 the highest peak tpl is at a time of around 3ms, which is approximate 2ms before the time of subframe 5. Therefore, the timing offset of the data x with respect to the frame of NB-IoT data is approximately 2ms. The technique described above is used to determine a coarse estimate of the timing offset up to a precision of plus or minus a half symbol.

An exemplary method will now be described in which a UE performs fine timing synchronisation of a received signal containing an NPSS. It is assumed that the UE has determined a coarse timing estimation prior to the implementation of the present method, and therefore that the timing of the received signal is known to a precision of at least plus or minus a half symbol.

As shown in Figure 6, the method for performing fine timing synchronisation begins at S4 in which the UE accumulates, at each of a set of memory locations, terms derived from samples taken from the received signal, thereby storing an accumulation value at each of the memory locations. In this example, the UE performs the accumulation in hardware, and each of the memory locations is a hardware register.

The received signal contains an NPSS having to a predetermined sequence of symbols, and this sequence of symbols has symmetries that make the received signal suitable for accumulation, as will be described hereafter. In the NB-IoT standard, subframe 5, which contains the NPSS, comprises two slots, each slot containing 7 symbols. The first symbol of each slot, labelled I = 0 and I = 7 respectively, are long symbols, and the remaining symbols of the subframe are short symbols. Each symbol in the subframe contains a cyclic prefix followed by an NPSS data component. The NPSS data component for each symbol contains M_Data samples corresponding to M_Databits of NPSS data. According to the NB-IoT standard, M_Data = 128. Long symbols have an extended cyclic prefix and short symbols have a regular cyclic prefix. A regular cyclic prefix contains M_{CP short} samples, resulting in a total of M_{sym short} = M_{CP s}hort + ^Data samples in a short symbol. An extended cyclic prefix contains M_CP;iong samples, resulting in a total of M_{sym long} = M_{CP long} + M_Data samples in a long symbol. The difference between the number of samples in a long symbol and the number of samples in a short symbol is given by M_Diff = M_sym [_ong — M_{sym short} = Mcpjong^— ^cp,short· According to the NB-IoT standard, M_{CP shor}t ⁼ 9 and M_{CP long} = 10.

Figure 7 illustrates time domain representations of three consecutive symbols of an NPSS according to the NB-IoT standard. Specifically, Figures 7a, 7b, and 7c illustrate symbols labelled Z = 6, Z = 7, and I = 8 respectively. As shown, each symbol contains a cyclic prefix followed by an NPSS data component. At a sampling rate of 1.92MHz, the NPSS data component for each symbol is sampled M_Data = 128 times, corresponding to 128 bits of NPSS data.

The symbol shown in Figure 7b has an extended cyclic prefix and the symbols shown in Figures 7a and 7c have regular cyclic prefixes. At a sampling rate of 1,92MHz, the regular cyclic prefixes of Figures 7a and 7c are each sampled M_{CP short} = 9 times. By contrast, the extended cyclic prefix of Figure 7b is sampled M_CP [_ong = 10 times. The difference between the number of samples in the symbol having an extended cyclic prefix and the number of samples in the symbols having a regular cyclic prefix is therefore given by M_Diff = M_CPlong - M_CPshort = 1.

The symbol of Figure 7b is related to the symbol of Figure 7a by a signal inversion and a truncation in which the first symbol of the extended cyclic prefix is discarded. The symbol of Figure 7c is related to the symbol of Figure 7a by a signal inversion. Each of the remaining non-zero symbols of the NPSS is either identical to the symbol of Figure 6a, or is related to the symbol of Figure 7b by a signal inversion. The present invention makes use of these symmetries of the NPSS symbols in order to accumulate terms derived from samples from a received signal.

Figure 8 schematically shows a subframe of an NPSS sequence according to the NPSS standard. The subframe contains two slots (slot 1 and slot 2) and each slot contains 7 symbols. The first symbol in each slot (Z = 0 for slot 1 and Z = 7 for slot 2) has an extended cyclic prefix containing M_CP [_ong samples. The remaining symbols in each slot each have a regular cyclic prefix containing M_{CP short} samples. The NPSS data components of the non-zero symbols (symbols with Z = 3 to Z = 13) are identical up to a sign change, due to the definition of the cover code (given in this example by Equation (2)). Therefore, multiplying each symbol by the corresponding term of the cover code, and truncating the first symbol in each slot by discarding the first M_Diffsamples, yields identical results each of the non-zero symbols in the subframe.

Figure 9 shows an example of a routine for accumulating, at S4, a set of terms derived from samples from a received signal, whereby to determine an accumulation value. In this example, the routine is performed for each of M_{sym short} accumulation values, resulting in one accumulation value being stored at each of Mjym.short memory locations. The routine begins by initialising, at S401, an index I and an accumulation value both to zero. The routine receives, at S402, a sample from the received signal. The routine derives, at S403, a term from the received sample. If the cover code component S(l) is equal to — 1, the routine derives the term by changing the sign of the sample. If 5(Z) is equal to 1, the term is equal to the value of the sample. If 5(Z) is equal to 0, the term is 0. As shown in Figure 8, in the example of an NPSS defined according to Equation (2), three cover code components (5(7),5(8), and 5(12)) are equal to —1.

The routine adds, at S404, the derived term to the accumulation value. The routine then skips, at S405, M_{sym i+1} samples, where M_{sym i+1} is the number of samples in symbol Z+l. In the example discussed above with reference to Figure 8, M_{sym i} = /^sym,long /^CP,long + ^Data ίθΓ Z 0 and Z 7, and ^sym,short ^cp,short + ^Data for all other values of I in the subframe. The routine increments, at S406, the value of Z by 1. The routine then returns to S402 with the incremented value of Z. The routine continues for all of the values of I in the subframe (until Z = 13, in the example of Figure 8), and the resulting accumulation value is stored. For the present example, the routine of Figure 9 includes a total of 11 complex additions (or alternatively, subtractions), corresponding to the 11 non-zero components of the cover code 5.

As mentioned above, the routine of Figure 9 is performed a total of M_{sym short}times, resulting in a set of M_{sym short} accumulation values, with the routine being initialised for successive accumulation values with successive initial samples. In the present example, in which the cover code 5 has 11 non-zero components, the total computational cost of the determining, at S4, a set of accumulation values is therefore

M_sym, short X 10 = 137 X 10 = 1507 complex additions. The total number of memory registers required for storing the set of accumulation values is M_{sym short} = 137.

In the present example, the accumulation value f(m) stored at the m^th memory location for m = 0,..., M_{sym short} — 1 is given by Equation (7):

/(m) = x(m + M_{CP diff}) · S(0) + ’ x(m + I · Af_{sym s}h_ort + Mqp_djff) · S(T) = 1 / A (⁷) + x(m + 7 · M_sym;Sh_ort 4 2 · Mqp_;djff) · S(7) + ’ x(m + I M_{sym s}h_ort + 2 · Wcp.diff) ’ = 8 where x is time domain data of the received signal, and x(i) is the i^th sample taken from the received signal. In this example, M_{sym short} = 137 and M_diff = 1.

Applying the routine of Figure 9, according to Equation (7), to an NPSS sequence with a timing offset of zero (such that x(0) is the first sample from the NPSS subframe), results in each term of each accumulation value being the same, and therefore the accumulation value is given by a multiple of any one of the terms (in this example, 11 times the value of any one of the terms). This is because the terms of each accumulation of terms are derived from samples taken from the received signal at timings corresponding to the predetermined sequence of symbols of the NPSS. The timings take into account both the extended cyclic prefix and the regular cyclic prefix such that one term is derived from each symbol of the predetermined sequence of symbols. In this case, the set of accumulation values therefore corresponds to a multiple of a single symbol of the NPSS.

In practice, the routine of Figure 9 is applied to a received signal containing an NPSS, where the timing offset of the received signal (which is equal to the timing offset of the NPSS contained within the received signal) may only be known to a precision of plus or minus a half symbol. Before the routine of Figure 9 is applied, the received signal is temporally shifted such that the timing offset is known to lie between minus a half symbol and plus a half symbol. The set of accumulation values given by Equation (7) will then approximate a multiple of a single time-shifted symbol of the NPSS.

The method of Figure 6 continues by determining, at S5, a cross-correlation between the set of accumulated values and data corresponding to a portion of the predetermined sequence of symbols. In this example, the portion corresponds to a single symbol of the predetermined sequence of symbols, and therefore the crosscorrelation is between a single NPSS symbol and a set of accumulation values that approximates a multiple of a time-shifted NPSS symbol. The cross-correlation contains a set of cross-correlation terms, each cross-correlation term corresponding to one of a set of candidate timing shifts. In this example, the timing shift is known to lie between minus a half symbol and plus a half symbol, and therefore the set of candidate timing offsets has a range equal to a duration of one symbol. Specifically, the set contains ^sym,short equally spaced candidate timing offsets range from minus a half symbol to plus a half symbol. In other examples, the coarse timing estimate may be more precise, in which case the set of candidate timing offsets would have a range of less that a duration of one symbol.

The cross-correlation is defined such that it has a large magnitude when the candidate timing offset is equal to the timing offset of the received signal. In the present example, the cross-correlation h(k) is defined by Equation (8):

h(k + K) = ^sym.short^-! (§) ’ f (τη) · g ((τη + k) % M_Sy_m;Short)’ m=0 for k = — K, —K + 1,..., K, where g*(m) is the complex conjugate of the m^th sample from the time domain representation of the predetermined NPSS sequence, and K is the number of samples corresponding to the maximum possible timing offset. In the present example, K = (M_symshort — 1)/2 = 68. In Equation (8), % denotes the modulo operator. As discussed above, Equation (8) cross-correlates the set of accumulation values with a single symbol of the NPSS sequence, and the set of accumulation values approximates a time-shifted symbol of the NPSS. This explains why the cross-correlation has a large magnitude for a particular value of k, which corresponds to the case in which the candidate timing offset is equal to the timing offset of the received signal. In this example, the computational cost of computing the crosscorrelation of Equation (8) is given by 137² = 18796 complex additions and 137² = 18796 complex multiplications.

The method of Figure 6 continues by determining, at S6, which of the set of candidate timing offsets corresponds to the timing offset of the received signal, thereby determining the timing offset of the received signal. The candidate timing offset corresponding to the timing offset of the received signal is that which results in the greatest magnitude of the cross-correlation. In the present example, the determined timing offset, T_offset, is given by Equation (9):

Offset = arg max(|/i(fc)|²) - K. (9) k

Figure 10 shows the results of an experiment in which the probability of a UE determining the correct timing offset of a received signal, using the method described above, was measured. In the experiment, signals with known timing offsets within the range -K to K were used, where K = 68, for three different SNR levels -5dB, -lOdB, and -15dB. The experiment was repeated 1000 times for each value of K at each SNR level. It is observed that the probability of determining the correct timing offset is close to one for any of the timing offsets when the SNR is -5dB or -lOdB. When the SNR is -15dB, the probability of determining the correct timing offset is close to one when the timing offset is relatively small, but is reduced for larger timing offsets. This is because, for larger timing offsets, the set of accumulation values less closely approximates a time-shifted multiple of anNPSS symbol, resulting in a reduced magnitude of the crosscorrelation. The experiment was also conducted at OdB SNR. The probability of determining the correct timing offset at OdB was equal to one for any of the timing offsets.

An alternative method for performing fine timing synchronisation is to omit the accumulation stage S4 of Figure 6, and simply to compute a cross-correlation between the received signal and a full subframe of the predetermined NPSS sequence. Although this alternative method may be used to accurately determine the timing offset, the computational cost is significantly greater than for the method according to the present invention. Since the subframe of the NPSS sequence contains a total of 1508 non-zero cover code components, the computational cost of computing the cross-correlation for the alternative method is given by 137 x 1508 = 206596 complex additions and 137 X 1508 = 206596 complex multiplications. Furthermore, the number of memory registers required to store the samples of the received signal for crosscorrelation for the alternative method is 1508. The method according to the present invention therefore provides a significant reduction in both the computational cost and the required number of memory registers, even when the additional stage accumulation stage S4 is included. Specifically, the present method reduces the number of complex multiplications by 90.9%, the number of complex additions by 90.3%, and the number of registers by 90.9%.

Figure 11 shows a UE 100 operable to perform fine timing synchronisation in accordance with the present invention. The UE 100 includes a receiver 110, a processing unit 120, accumulation circuitry 130, and memory 140, all of which are connected to a system bus 150. The receiver 110 is configured to receive a signal within a frequency band. The processing unit 120 is configured to detect an NPSS and to determine a coarse timing estimate, in accordance with S1-S3 of Figure 4. In this example, the accumulation circuitry 130 is hardware circuitry configured to derive terms of each of a set of accumulation values from samples of the received signal, and to accumulate the derived terms to determine the accumulation values. The memory 160 includes hardware registers configured to store the set of accumulation values. The processor 120 is further configured to determine, in response to receiving an indication from the accumulation circuitry that the accumulation values have been determined, a cross-correlation between the set of accumulation values and data corresponding to a portion of the predetermined sequence of symbols of the NPSS, and to determine, from the cross-correlation, which of a set of candidate timing offsets corresponds to the timing offset of the received signal.

The above embodiments are to be understood as illustrative examples of the invention. Further embodiments of the invention are envisaged. For example, in some embodiments determining the set of accumulation values is performed in software rather than in hardware. It is to be understood that any feature described in relation to any one embodiment may be used alone, or in combination with other features described, and may also be used in combination with one or more features of any other of the embodiments, or any combination of any other of the embodiments. Furthermore, equivalents and modifications not described above may also be employed 5 without departing from the scope of the invention, which is defined in the accompanying claims.

Claims

1. A method of determining a timing offset of a received signal comprising a Narrowband Primary Synchronisation Signal (NPSS), the NPSS having a predetermined sequence of symbols, the method comprising:

storing a set of accumulation values, an accumulation value in the set comprising an accumulation of terms, terms in the accumulation of terms being derived from samples taken from the received signal at timings corresponding to the predetermined sequence of symbols;

determining a cross-correlation between the set of accumulation values and a portion of the predetermined sequence of symbols; and determining, from the cross-correlation, which of a set of candidate timing offsets corresponds to the timing offset of the received signal.

2. The method of claim 1, wherein symbols of the predetermined sequence of symbols comprise an NPSS data component, the NPSS data components being identical to each other up to a signal inversion, and wherein the accumulation of terms takes account of the signal inversion.

3. The method of claim 2, wherein taking account of the signal inversion comprises performing a change of sign in the accumulation of terms at a point corresponding to the signal inversion.

4. The method of any previous claim, wherein the portion of the predetermined sequence of symbols corresponds to a symbol of the predetermined sequence of symbols, and wherein the set of candidate timing offsets has a range of less than or equal to a duration of one symbol.

5. The method of any previous claim, wherein each of the plurality of symbols comprises a cyclic prefix, one or more of the cyclic prefixes being an extended cyclic prefix and the remaining cyclic prefixes being regular cyclic prefixes, and wherein said timings, corresponding to the predetermined sequence of symbols, take into account both the extended cyclic prefix and the regular cyclic prefix.

6. The method of claim 5, wherein at least one sample with a timing corresponding to an extended cyclic is omitted from the set of accumulation values.

7. The method of any previous claim, wherein the predetermined sequence of symbols comprises data representable in the frequency domain as: