Technical Field

The present disclosure relates to a method for estimating a carrier frequency offset of a received signal. In particular, but not exclusively, the present disclosure relates to a method for estimating a carrier frequency offset of a received Narrowband Internet of Things (NB-IoT) signal.

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 predetermined frequency 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 a carrier frequency offset (CFO). The CFO Af is the difference between the frequency / that the base station transmitter radio is tuned to, and the frequency / that the UE receiver radio is tuned to, such that Af = f— f. At the UE, the CFO appears as a signal perturbation that obstructs the UE from decoding the received signal.

Having performed timing synchronisation and estimated the CFO during the initial attempt to connect, the UE recalculates the CFO estimate repeatedly during data transfer, as the CFO may vary over time. The CFO estimate is typically recalculated using a reference signal. In some cases, the CFO is recalculated using the NPSS. The NPSS is transmitted once every radio frame (i.e. with a period of lOms), and contains 121 resource elements. The NPSS therefore includes a sufficient number of data points for relatively accurate CFO estimation, but only allows for the CFO to be estimated once every radio frame. In other cases, the CFO estimate is recalculated using a Narrowband Reference Signal (NRS). An NRS is transmitted once every subframe (i.e. with a period of lms), and contains either 8 resource elements (in the case of a single NRS port) or 16 resource elements (in the case of two NRS ports). An NRS therefore includes fewer data points leading to less accurate CFO estimation, but allows for the CFO to be recalculated more frequently.

Summary

According to a first aspect, there is provided a method of determining an estimated carrier frequency offset of a received downlink signal which is arranged in subframes. The received downlink signal comprises a plurality of subframes each comprising a repeated data sequence. The method includes: identifying a plurality of subframes which each comprise a repeated data sequence; receiving first symbols of a first subframe of the plurality of subframes; receiving second symbols of a second subframe of the plurality of subframes; determining a correlation between components of the received first symbols and components of the received second symbols, and determining, from the correlation, the estimated carrier frequency offset.

Identifying subframes having a repeated data sequence allows for more frequent estimation of the CFO than for methods which rely on sparsely-transmitted reference signals, such as the NPSS in a downlink NB-IoT signal. Frequent estimation of the CFO is desirable when the CFO is likely to vary with time. Furthermore, the repeated data sequence may include significantly more resource elements than some reference signals, such as the NRS in a downlink NB-IoT, allowing for more accurate estimations of the CFO than methods which rely on such reference signals.

According to an example, a received downlink signal is deployed in a multicarrier configuration, and the present method allows for CFO estimation the using a secondary carrier configured in a non-anchor mode. In some examples, a signal on a carrier configured in a non-anchor mode omits subframes containing synchronisation data and broadcast data, and therefore has more available subframes for other data, such as shared channel data or control channel data. Therefore, determining an estimated CFO using a signal on a carrier configured in a non-anchor mode, without requiring the UE to switch to an anchor carrier, allows a UE to receive the shared channel data or control channel data at a higher rate compared with an example in which a UE is required to switch to an anchor carrier to determine an estimated CFO.

According to a second aspect, there is provided a device operable to determine an estimated carrier frequency offset of a received downlink signal which is arranged in subframes. The device includes processing circuitry configured to: identify a plurality of subframes which each comprise a repeated data sequence; receive first symbols of a first subframe of the plurality of subframes; receive second symbols of a second subframe of the plurality of subframes; determine a correlation between components of the received first symbols and components of the received second symbols, and determine, from the correlation, the estimated carrier frequency offset.

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

Brief Description of the Drawings

Figure 1 is a block diagram illustrating time multiplexing in frames of a downlink NB-IoT signal.

Figure 2 shows a resource map illustrating an example of resource element allocation in an NB-IoT signal configured for standalone deployment.

Figure 3 shows a resource map illustrating an example of resource element allocation in an NB-IoT signal configured for in-band deployment.

Figure 4 is an Argand diagram showing two received symbol components in a received downlink signal.

Figure 5 is a block diagram showing a UE operable to determine a CFO estimate.

Figure 6 is a flow diagram showing an exemplary routine for determining a CFO estimate.

Figure 7 is a flow diagram showing an exemplary routine for receiving and processing data in a received downlink signal. Figure 8 is a plot of cumulative frequency distributions of empirical CFO estimation errors for a simulated signal with Additive White Gaussian Noise (AWGN).

Figure 9 is a plot of cumulative frequency distributions of empirical CFO estimation errors for a simulated signal using the Extended Pedestrian A (EPA) model with a 5Hz maximum Doppler spread.

Figure 10 is a plot of cumulative frequency distributions of empirical CFO estimation errors for a simulated signal using the Extended Typical Urban (ETU) model with a 5Hz maximum Doppler spread.

Figure 11 is a plot of Root Mean Square Errors (RMSEs) in CFO estimates for a simulated signal with Additive White Gaussian Noise (AWGN).

Figure 12 is a plot of Root Mean Square Errors (RMSEs) in CFO estimates for a simulated signal using the Extended Pedestrian A (EPA) model with a 5Hz maximum Doppler spread.

Figure 13 is a plot of Root Mean Square Errors (RMSEs) in CFO estimates for a simulated signal using the Extended Typical Urban (ETU) model with a 5Hz maximum Doppler spread.

Detailed Description

Figure 1 illustrates time multiplexing between physical channels and signal in a downlink NB-IoT signal. In the illustrated example, the downlink NB-IoT signal is deployed on an anchor carrier, and accordingly includes synchronisation data and broadcast information. The downlink signal is arranged into numbered frames, each frame having a duration of lOms. Each frame is arranged into 10 subframes numbered from 0 to 9, each subframe having a duration of lms. As shown, subframe 0 of an even numbered frame contains the Narrowband Physical Broadcast Channel (NPBCH). Subframe 5 of the even numbered frame contains the Narrowband Primary Synchronisation Signal (NPSS). Subframe 9 of the even numbered frame contains the Narrowband Secondary Synchronisation Signal (NSSS). The remaining subframes of the even numbered frame contain Narrowband Physical Downlink Shared Channel (NPDSCH) data or Narrowband Physical Downlink Control Channel (NPDCCH) data. An odd numbered frame is arranged similarly to the even numbered frame, but subframe 9 contains NPDSCH data or NPDCCH data, as opposed to the NSSS. A downlink NB-IoT signal may be deployed in a multicarrier configuration, including an anchor carrier (for example, an anchor carrier arranged as shown in Figure 1), and a secondary carrier configured in a non-anchor mode. The secondary carrier may omit the NPBCH, the NPSS, and the NSSS, such that every subframe contains NPDSCH or NPDCCH data. If such a deployment is used, a UE may initially connect to the anchor carrier to perform initial timing synchronisation, and once connected, may switch to the secondary carrier in order to receive NPDSCH or NPDCCH data at a higher rate.

Figure 2 shows a resource map illustrating an example of resource element allocation in an NB-IoT signal, for a subframe containing NPDSCH data or NPDCCH data. The subframe contains 14 symbols labelled l and 12 subcarriers labelled k = 0, ... , 11. The subframe therefore contains a total of 168 resource elements. In this example, the NB-IoT signal is configured for standalone deployment, and the subframe is dedicated entirely to the NB-IoT signal. In this example, 8 resource elements are used for each of two NRS ports, resulting in 152 resource elements free to be used for NPDSCH data or NPDCCH data. In another example, only one NRS port is used, leaving 160 resource elements free to be used for NPDSCH data or NPDCCH data.

Figure 3 shows a resource map illustrating another example of resource element allocation in an NB-IoT signal, again for a subframe containing NPDSCH data or NPDCCH data. In this example, the NB-IoT signal is configured for in-band deployment, and therefore shares the subframe with a Fong Term Evolution (FTE) carrier. In this example, 8 resource elements are used for each of two NRS ports, 20 resource elements are used for the FTE Cell- specific Reference Signal (CRS) and 28 resource elements are used for FTE Physical Downlink Control Channel (PDCCH) data, leaving 104 resource elements free to be used for NPDSCH data or NPDCCH data.

As shown in Figure 1, subframes containing NPDSCH data or NPDCCH data are transmitted more frequently than subframes containing the NPSS. Furthermore, as shown in Figures 2 and 3, the number of resource elements allocated in a subframe to NPDCCH data or NPDSCH data is comparable to the number of resource elements allocated in a subframe to the NPSS. Unlike the NPDSCH data and the NPDCCH data, however, the NPSS has a predetermined sequence that is generally known to a UE receiving an NB-IoT signal. This facilitates a hypothesis-testing method for estimating the CFO offset, in which a received NPSS is compared with candidate NPSS sequences with a range of frequency offsets.

Although NPDSCH data and NPDCCH data do not have a predetermined sequence known to a UE, several NPDSCH or NPDCCH subframes may each contain a repeated data sequence, such that a UE may accumulate the repeated data sequence over the NPDSCH or NPDCCH subframes in order to artificially reduce the Signal to Noise Ratio (SNR). In some applications, UEs are deployed in locations having a very low SNR (e.g. lower than OdB, lower than -5dB, or lower than -lOdB). Such applications include smart electricity meters or smart gas meters located in basements or other enclosed areas of buildings.

The present invention makes use of data sequences repeated between subframes in order to determine an estimated CFO offset of a received downlink signal. The method includes identifying a plurality of subframes each having a repeated data sequence, and determining a correlation between symbols received from a first subframe of the plurality of subframes and symbols received from a second subframe of the plurality of subframes, and determining, from the correlation, the estimated frequency offset.

Figure 4 illustrates an example which a first Quadrature Phase-Shift Keying (QPSK) symbol component b _{k i n} is transmitted at time t = 0 on a subcarrier in the n ^th subframe of a signal. The symbol component b _{k l n} takes up a single resource element in the frequency domain representation of the transmitted signal. In this example, there is a CFO of Af between the base station transmitting the signal and a UE receiving the signal. The UE receives the signal at time t = t _r . Neglecting the effects of fading, noise, and other perturbations to the signal, the UE receives a first symbol component b _k,i,n ⁼ In this example, a second QPSK symbol component b _k>i>m is transmitted at a later time t = At on a subcarrier in the m ^th subframe of the signal. The UE receives a second symbol component b _k In this example, the n ^th subframe and the m ^th subframe each have a repeated data sequence, such that the transmitted symbol components are equal, with b _{k i n} = b _{k l m} . The received symbol components b _k>i>n and b _{k i m} are shown in the Argand diagram of Figure 4. The angle Q between the lines representing and b _{k i m} is given by Q = 2 pD/Dί. Therefore, a crude estimate of the CFO, using the symbol component repeated between the n ^th subframe and the m ^th subframe, is given by D/ _{h ίh} = q / (2pDί) = ^ar g(¾,i, _m ¾i _,n )/ (2pDί).

Due to corruption of a received signal by interference and noise, using a single data point from a data sequence repeated between two subframes, as described above, is unlikely to give an accurate estimate of the CFO in a practical setting. A more accurate estimate may be achieved by determining a correlation including multiple data points from the repeated data sequence, such that the effects of interference and noise are substantially averaged out and have less effect on the estimate. In the present example, a suitable correlation C _{n m} is given by Equation (1): where the double sum over symbol number l and subcarrier number k includes M symbol components in the repeated data sequence, each symbol component taking up a respective resource element. The more accurate estimate of the CFO is determined from the correlation C _{n m} as f _{n m} = arg(C _{n m} )/(27rAt).

In some examples of signals arranged in subframes each having a repeated data sequence, symbols in the subframes have associated data components and associated scrambling coefficients, where the associated data components are repeated between the subframes, but the scrambling coefficients are generally different. The scrambling coefficients have a predetermined sequence known to the UE receiving the signal, such that the UE can descramble the signal in order to recover the data sequence. Including scrambling coefficients in a signal reduces detrimental effects caused by interference. In particular, signals transmitted from base stations in neighbouring cells may include repetition, and therefore interference effects from such signals may accumulate as a UE accumulates data from the intended received signal. Scrambling coefficients introduce pseudo-randomness to the signal such that interference from neighbouring cells (or other signals having data repetitions corresponding to those of the intended received signal) does not accumulate, and the detrimental effects of interference are thereby mitigated.

For examples in which symbols of subframes have associated data components and associated scrambling coefficients, determining an estimated CFO in accordance with the present invention may include taking account of the associated scrambling coefficients. In particular, some examples include determining a correlation that takes account of the associated scrambling coefficients. In some examples, scrambling coefficients have values of either 1 or—1, and therefore taking account of scrambling coefficients involves a UE performing a change of sign of terms in a correlation such that the correlation is between associated data components.

In an example of a downlink NB-IoT signal, the k ^th subcarrier of the ^th transmitted Orthogonal Frequency Division Multiplex (OFDM) symbol in the n ^th NPDSCH/NPDCCH subframe is denoted a _{fe i n} and is given by Equation (2): where E +1/V2 are real and imaginary parts of a data component of the encoded symbol, and s _n E ±1 are scrambling coefficients that multiply the real and imaginary parts of the associated data component.

In this example, there is a CFO of Af between a base station transmitting the downlink NB-IoT signal and a UE receiving the downlink NB-IoT signal. The UE receives the downlink NB-IoT signal at time t = t _r . At the UE, the received symbol is assumed to have faded by a factor h _{k l n} due to a fading channel h(t), and is further assumed to be corrupted by additive complex Gaussian noise n _{fe i n} ~ CJ\T (0, s ² ), where s ² = E(|n _{fe i n} | ² ) is the variance. The UE therefore receives a symbol component a _{k t >n} given by Equation (3): In this example, a second symbol component a _k ^ _m is transmitted at a later time t = At on the same subcarrier in the m ^th subframe of the signal, and is given by Equation (4): where s _{k (rl) m} , s _{k ( i l )rn} E ±1. As shown by Equation (4), the real and imaginary parts of the data components of a _{k j m} are identical to the data components of a _{k l n} . However, f (i)

the scrambling coefficients s _{k l m} , s _{k l m} are not necessarily the same as the scrambling

( ) _(i)

coefficients s _{k l n} , s _{k l n} . Accordingly, in this example, determining an estimated CFO includes taking account of the associated scrambling coefficients.

In this example, if the scrambling coefficients of a _{k t m} and CL _{k i n} are equal such that s then a _{k l m} = a _{k l n} . If the scrambling coefficients of a _{k m} and a _{k l rn} are opposite such that then ^a _k,i,m ^{= ~a} _k,i,n I ⁿ order to take account of the scrambling coefficients, a descrambling array / is introduced, which has components given by descrambling numbers I(k, l, n, m). The descrambling numbers / (k, l, n, m) are defined by Equation

(5):

Using Equations (2), (4), and (5), it is observed that if the scrambling coefficients of a _k i _m are equal or opposite to the scrambling coefficients of CL _k>i>m , then

The UE receives a second symbol component a _{k t m} given by Equation (6):

It is assumed that the fading channel varies slowly with time, such that /i(t) « h(t + At), and hence the fading factor h _{k l rn} is approximately equal to the fading factor h _k,i,n This is expected to be the case provided that the time difference At between the n ^th subframe and the m ^th subframe is not too great. Equation (7) then holds approximately if the scrambling coefficients of a _k i _m and CL _k>i>n are equal such that ^s k,i.m = ^s kln ^{and s} kim ^{= s} k].n ^{or if the} scrambling coefficients of a _{k l rn} and a _{k l n} are opposite such that sg _m = s^ln ^{and s} klm = ^~5 ΐIh ·

T ^fl k,l,mVk,l,n·

Using the circular symmetry of the random Gaussian variable n _k ^ _m , the expectation value of argument of the sum of terms in Equation (7) is given by E(arg( _Tn a _{k l n} ) ) = 2pD/Dί. This observation prompts two possible estimates of the CFO, both of which fall within the scope of the present invention. The first estimate of the CFO is given by Equation (8):

K- i L— i

1 f 1

fn.m bb å å arg(

2pDΐ

l ⁿ ' ^m _f c=o i (

=0 8)

The second estimate of the CFO is given by Equation (9):

In both of the estimates above, K is the number of subcarriers and L is the number of symbols in a subframe. For an NB-IoT subframe, K = 12 and L = 14. M _n ,m is the number of non-zero descrambling numbers / (k, l, n, m) in the respective double sum, as given by Equation (10):

Since the scrambling coefficients are pseudo-random, the expected value of M _{n m} , and hence the approximate expected number of data points that can be used in the CFO estimation, is given by KL/2. For an NB-IoT subframe with K = 12 and L = 14 the expected number of data points is given by E = 84. In practice, for a downlink NB-IoT signal, the number of data points is less than this expected number, due to the fact that not all of the resource elements in the signal contain NPDSCH/NPDCCH data (some resource elements contain, for example, NRS data or LTE data) and hence symbol components from some of the resource elements may not be included in the correlation.

The estimate of Equation (9) has favourable implementation properties in comparison with estimate of Equation (8). In Equation (9), the argument of the correlation (the part in brackets) is computed after the terms in the correlation have been summed. In Equation (8), the argument of each of the M _{n rn} terms is computed and then added to the correlation. Computing the estimate of Equation (9) is therefore less computationally expensive than computing the estimate of Equation (8). The computational cost of implementing Equation (9), in an example in which 160 resource elements are available, is approximately 80 complex multiplications, 2 divisions, and one complex angle computation. NB-IoT UEs may have limited processing power, or limited battery power, and therefore reducing computational cost is desirable. Furthermore, if the argument of one or more of the terms in the estimate of Equation (8) is greater than p radians, branching effects due to the branch cut of the argument function may result in erroneous results being produced.

The estimate of Equation (9) is suitable for estimating a CFO satisfying |D/| < 1/(2Dί). For larger CFOs, the branch cut of the multivalued argument function leads to branching of the right hand side of Equation (9), such that the estimated CFO cannot be uniquely determined without additional information. In an example in which adjacent NPDSCH/NPDCCH subframes are used in an NB-IoT signal, At = 1ms and therefore Equation (9) is suitable for estimating a CFO satisfying |D/| < 500Hz. If non-adjacent subframes are used, the range of CFOs for which Equation (9) is useful becomes smaller.

Figure 5 shows an example of a UE 100 operable to determine an estimated CFO of a received downlink signal in accordance with the present invention. The UE 100 includes a receiver 110, a processing unit 120, and memory 130, connected by a system bus 140.

Figure 6 shows an exemplary routine performed by the processing unit 120 of the UE 100 in order to determine an estimated CFO of a received downlink signal.

The processing unit 120 initialises, at S601, a correlation value in the memory 130 to zero. The processing unit 120 identifies, at S602, a plurality of subframes having a repeated data sequence in the received downlink signal. In this example, subframes having a repeated data subframe are identified using scheduling information embedded within the received downlink signal. In this example, the scheduling information is included in a System Information Block (SIB) within the received downlink signal. The processing unit 120 receives, at S603, first symbols from a first subframe of the plurality of subframes, and receives, at S604, second symbols from a second subframe of the plurality of subframes, the first symbols and the second symbols having repeated associated data components. The received first symbols and the received second symbols have associated data components and associated scrambling coefficients, the associated data components being repeated between the first subframe and the second subframe. The associated data components received by the UE 100 are the data components of the corresponding symbols transmitted by the base station. The processing unit 120 computes, at S605, a term to be added to the correlation stored in the memory 130. In this example, the term in the correlation includes a product of a first symbol component from the first subframe and a complex conjugate of a second symbol component from the second subframe. In this example, computing the term includes taking account of the associated scrambling coefficients. In particular, taking account of the associated scrambling coefficients includes performing a change of sign of the term if the scrambling coefficients of the first symbol component and the second symbol component are equal, and discarding the term if the scrambling coefficients of first symbol component and the second symbol component are neither equal nor opposite. The processing unit 120 adds, at S606, the computed term to the correlation value stored in the memory 130. The processing unit repeats steps S605 and S606 for every symbol component of the symbols received from the first and second subframes, thereby determining a correlation between the first symbols and the second symbols.

The processing unit 120 determines, at S607, the CFO estimate from the correlation. In this example, determining the CFO estimate includes determining an argument of the correlation, and the determined CFO estimate is proportional to the determined argument of the correlation.

As mentioned above, in some examples a UE performs timing synchronisation and determines an initial CFO estimate during an initial attempt to connect to a base station. The UE then recalculates the CFO estimate repeatedly during data transfer, as the CFO may vary over time. In some examples in accordance with the present invention, a downlink NB-IoT signal is deployed in a multicarrier configuration including an anchor carrier and a secondary carrier. In such an example, the UE performs timing synchronisation and determines the initial CFO estimate using an NPSS detected on the anchor carrier. Having performed the timing synchronisation and determined the initial CFO estimate, the UE switches to the secondary channel to receive NPDSCH or NPDCCH data. In this example, the secondary carrier is configured in a non-anchor mode and omits the NPBCH, the NPSS, and the NSSS, and every subframe on the secondary carrier includes NPDSCH or NPDCCH data. The UE may then recalculate the CFO estimate as often as once every subframe using the disclosed method, and optionally may perform frequency compensation. During frequency compensation, the frequency of the UE receiver radio is adjusted, using the CFO estimate, to match the frequency of the base station transmitter radio. In one example, a UE performs frequency compensation every time the UE recalculates the CFO estimate. In another example, a UE performs frequency compensation when a calculated CFO estimate exceeds a predetermined threshold. By repeatedly performing CFO estimation and frequency compensation, a UE can ensure that the CFO remains within a range in which the present method is applicable, and therefore the UE can continue to receive data on the secondary carrier without switching back to the anchor carrier. Figure 7 shows an exemplary routine performed by the UE 100 in order to receive data from a downlink NB-IoT signal. The UE 100 performs, at S701, a frequency band scan and detects, at S702, the downlink NB-IoT signal. In this example, the downlink NB-IoT signal is deployed in a multicarrier configuration. The UE 100 attempts to connect to the base station, and in doing so performs, at S703, initial synchronisation. Performing initial synchronisation involves the UE 100 detecting an NPSS on the anchor carrier of the downlink NB-IoT signal, and using the detected NPSS to perform timing synchronisation and to determine an initial CFO estimate.

Having performed initial synchronisation, the UE 100 switches to a secondary carrier of the multicarrier signal and receives, at S704, data from the multicarrier signal. In other examples, a UE may instead continue to receive data from the anchor carrier. The secondary carrier is arranged in subframes containing NPDSCH or NPDCCH data, with some of the subframes having repeated data sequences. The UE 100 extracts, at S705, symbols from the signal on the secondary carrier, and removes cyclic prefixes from the symbols.

The UE 100 performs, at S706, a 16 point Fast Fourier Transform (FFT) operation on the extracted symbols of the secondary carrier, in order to extract symbol components in the frequency domain for each of the subcarriers. The UE 100 performs, at S707, channel estimation. In this example, performing channel estimation includes detecting an NRS in the received data, and comparing the detected NRS to a predetermined NRS sequence stored by the memory 130 in order to correct for phase and amplitude variations resulting from the propagation of the signal from the base station to the UE 100. The UE 100 performs, at S708, equalisation of the signal and performs, at S709, soft bit demodulation in order to map each received signal component to a complex value in a discrete set of values according to the modulation scheme. In this example, QPSK modulation is used and each symbol component is mapped to one of the four complex numbers in the set {±1/V2 ± j 1/V2). The UE 100 removes, at S710, the scrambling coefficients from the symbol components, thereby recovering the associated data components of the symbols.

In addition to performing the operations S707-S710, the UE 100 performs, at S711, CFO estimation using the symbol components extracted at S706. In this example, the UE 100 determines a CFO estimate for each pair of consecutive subframes having a repeated data sequence, using the method described above with reference to Figure 6. In order to perform the CFO estimation according to the method of Figure 6, the UE 100 must simultaneously store two subframes worth of data in the memory 130.

Using the determined CFO estimate, the UE 100 performs, at S712, frequency compensation, which includes adjusting the tuning of the receiver 110. By repeatedly performing CFO estimation and frequency compensation, the UE 100 ensures that the CFO remains within a range in which the present method is applicable.

In some examples, more than two subframes may have the same repeated data sequence. This is likely in situations where UEs are expected to be deployed in locations with very low SNR, and where a relatively low data transfer rate is sufficient. In such examples, a UE may determine several CFO estimates using different combinations of subframes. A UE may then determine an average of the determined CFO estimates in order to determine an average CFO estimate.

In one example, a received downlink signal includes iV _rep subframes having a repeated data sequence. A method of determining a CFO estimate then includes determining multiple correlations, each correlation being between symbols of a first respective subframe and symbols of a second respective subframe. The method includes determining, from each of the plurality of correlations, a respective CFO estimate, and determining an average of the respective CFO estimates. Using multiple combinations of subframes in this way may lead to a more accurate CFO estimate. However, determining an average of multiple CFO estimates results in a higher computational cost in terms of number of operations and also in terms of memory required to store data for multiple subframes.

In examples in which a received downlink signal includes symbols having associated data components and associated scrambling coefficients, using multiple combinations of subframes may allow for more of the resource elements in a subframe to be used for CFO estimation, because different terms in a correlation will be discarded for each combination of subframes. For example, in the examples of Equation (8) and (9), the descrambling numbers I(kJ, n, m ) for different combinations of n, m will be non-zero for different values of k, l. In one example, iV _rep consecutive subframes have a repeated data sequence. In this example, a method includes determining an estimated CFO using each pair of adjacent subframes, and determining an average estimated CFO using Equation (11):

More generally, in an example in which multiple subframes have a repeated data sequence, a method includes determining an estimated CFO for each pair of subframes ( n , m) £ S, where S is a predetermined set of pairs, and determining an average estimated CFO using Equation (12): in which w _{n m} is a weighting assigned to the pair ( n, m ). In some examples, w _{n m} = 1/|S| for all pairs, resulting in a simple average. In other examples, w _{n n} depends on (n, r ) in order to prioritise more recently determined CFO estimates. Weighting an average CFO estimate in order to prioritise more recently determined CFO estimates may be appropriate if the CFO is expected to vary over time.

In one example, iV _rep consecutive subframes, labelled n = 1, , /V _rep , have a repeated data sequence. The set S includes each of the iV _rep — 1 pairs of adjacent subframes, and the weightings are assigned as w _{1 2} = (1— a) ^Nre P ^~2 and w _{n n+1} = a( 1— a) ^{Nre p_n_1} for n = 2, ... iV _rep — 1, where 0 < a < 1. Equation (12) then gives an exponential moving average, which is weighted to prioritise more recently determined CFO estimates. A skilled person will appreciate that an exponential weighted moving average may be determined efficiently by recursively using previously determined exponential moving averages.

Figures 8 to 10 show results of experiments in which Monte Carlo simulations were performed in order to generate simulated signals, and for each simulated signal the present method was performed in order to determine a CFO estimate. A large number of such experiments were performed in order to determine empirical probability density functions of the error e in CFO estimation, given by e = Af — Af, using the method of Equation (9) in conjunction with Equation (11). In each case, the simulated signal was an NB-IoT downlink signal configured for standalone deployment in a non anchor mode, with subframes containing NPDCCH data having a repeated. One NRS antenna port was included, such that 160 resource elements were available in each subframe for CFO estimation. The actual CFO in each case was lOOHz, the average SNR of the simulated signal was OdB.

Figure 8 shows cumulative density functions for the absolute estimation error | | for simulated signals including Additive White Gaussian Noise (AWGN), using different numbers of data repetitions iV _rep = 2, 4, 8, 16. As expected, it is observed that the performance improves for higher numbers of repetitions. For 2 repetitions, 40% of the absolute estimation errors are less than lOHz, and 95% of the absolute estimation errors are less than 40Hz. For 16 repetitions, more than 95% of the absolute estimation errors are less than lOHz.

Figure 9 shows cumulative density functions for the absolute estimation error | | for simulated signals using the Extended Pedestrian A (EPA) model with a 5Hz maximum Doppler spread. Figure 10 shows cumulative density functions for the absolute estimation error |e| for simulated signals using the Extended Typical Urban (ETU) model with a 5Hz maximum Doppler spread. It is observed that the performance of the method for the simulated AWGN signal is slightly better than for the simulated EPA and ETU signals. This is because fading channels of the EPA and ETU signals have a phase shift that varies with time. For higher Doppler shifts, the effect of this variation is stronger. In particular, if the assumption that the fading channel is slowly varying such that h(t) ~ h(t + At) does not hold, the accuracy of the CFO estimation suffers more in the cases of EPA and ETU signals. In such cases, it is recommended to use adjacent subframes to determine the CFO estimates, thereby minimising At.

Figures 11 to 13 show further results of experiments using simulated signals as described above. For Figure 11 to 13, the SNR (defined here as the average energy per symbol divided by the noise power spectral density) was artificially varied from -lOdB to lOdB, and the Root Mean Square Error (RMSE) is plotted for the three different signal models. It is observed that the RMSE tends to zero as the SNR increases. For lower values of SNR, the improvement in accuracy achieved by using more repetitions becomes greater. As before, the performance of the method for the simulated AWGN signal, illustrated by Figure 11, is slightly better than for the simulated EPA and ETU signals, illustrated by Figures 12 and 13 respectively.

The above embodiments are to be understood as illustrative examples of the invention. Further embodiments of the invention are envisaged. For example, the described methods may be performed by software or by an application- specific integrated circuit (ASIC) of a UE. 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 without departing from the scope of the invention, which is defined in the accompanying claims.