Methods and control units for determining an absent part of a bin coefficient of a first complex frequency-domain signal

Abstract

A method for determining a second part of a bin coefficient of a first complex frequency-domain signal (6a), wherein only a first part of a real part and an imaginary part is included in each bin coefficient, wherein a second part of the real part and the imaginary part is absent, the method being performed by a control unit (1), the method comprising: receiving (302) the first complex frequency-domain signal (6a); determining (304) the absent second part of each bin coefficient of the first frequency-domain signal (6a) based on the first part of the complex coefficient of adjacent bins of the bin being determined; adding (306), for each bin of the first complex frequency-domain signal, the determined second part to each bin coefficient, so that each bin coefficient of the first complex frequency-domain signal comprises both the real and the imaginary part.

Description

METHODS AND CONTROL UNITS FOR DETERMINING AN ABSENT PART OF A BIN COEFFICIENT OF A FIRST COMPLEX FREQUENCY-DOMAIN SIGNAL TECHNICAL FIELD

[0001] The present disclosure relates generally to methods and control units for determining an absent part of a bin coefficient of a first complex frequency-domain signal. The present disclosure also relates to computer programs and carriers corresponding to the methods and control units. BACKGROUND

[0002] Transform coding is a technique used to compress data from a data source. Common applications of transform coding include various audio coding standards. A transform coding scheme is suitable for handling complex baseband signals, so that it can be used in cellular base stations. In general, transform coding usually operates on input data with overlapping frames, applies a time- domain analysis window which is typically with a bell-shaped tapering function, followed by a Fourier transform and sometimes also a frequency-domain window. As for the input data with overlapping frames, it is common to use 50% overlap between input frames. The output of the Fourier transform is a complex frequency- domain signal having a frequency range. The frequency range can be divided into multiple sub-ranges named bins. Each bin has an index and complex coefficient. The bin coefficient represents the complex frequency-domain signal in its frequency range. Therefore, all the bins with corresponding coefficients represent the output complex frequency-domain signal. The redundance caused by the overlap in input data is mitigated by only keeping the real part or only the imaginary part of bin coefficient of the complex output signal of the transform encoder. The transform coding will be discussed in detail in the DETAILED DESCRIPTION part.

[0003] Since the output of the transform coding is a complex frequency-domain signal with only the real part or only the imaginary part in the bin coefficient, there is a need to determine / estimate the missing part, either real or imaginary, of thebin coefficient, so that the bin coefficient of the output complex frequency-domain signal becomes complete.

[0004] As for complex frequency-domain signals, signal correlation is an important application. Correlation techniques can be effective to determine e.g., time-difference, phase-difference, and / or magnitude ratio between two signals, e.g., a received signal and a reference signal. The reference can be another received signal, or an a priori known signal, where the latter is sometimes called a synthetic reference.

[0005] There are at least two ways of performing correlation of two signals. One is time-domain correlation and the other one is frequency-domain correlation. For time-domain correlation, it involves convolution operations, which often means high computational complexity. Further, for transform coded frequency-domain signals, each signal would have to be decoded before the convolution. For signals that are to be correlated, this means additional complexity increase since it is no longer sufficient to have only one single decoder. Therefore, time-domain correlation for transform encoded signals is not desirable.

[0006] As for frequency-domain correlation, calculating cross-correlation in frequency-domain by elementwise multiplication with the complex conjugate of the reference typically has lower computational complexity than performing a convolution in time-domain. Therefore, the frequency-domain correlation is more desirable in this scenario. However, since the transform coded complex signals only comprises the real part or the imaginary part in the bin coefficient, the frequency-domain correlation becomes difficult. The result of the frequency- domain correlation also only comprises a real part or an imaginary part, which in turn causes an ambiguity in time-domain due to aliasing.

[0007] In order to overcome the disadvantage of the frequency-domain correlation mentioned above, in prior art, a method is proposed to estimate the imaginary part of the cross-correlation by multiplying bins from adjacent transform frames in time. This method works well, but some Signal-to-noise ratio (SNR) loss is observed compared with the case where each signal is first decodedindividually, and then calculating correlation in time-domain. If the effective overlap of adjacent transform frames is small, i.e., narrow bell-shape for the time-domain analysis window is used to improve sidelobe suppression, the SNR loss becomes larger since the uncertainty in the imaginary part of the frequency-domain cross- correlation increases.

[0008] Therefore, there is also a need to provide an improved frequency-domain correlation method for transform coded complex frequency-domain signals which only comprises the real part or the imaginary part in the bin coefficient.

[0009] In summary, there is a need to provide a solution for determining the absent real or imaginary part of a bin coefficient of a complex frequency-domain signal which is output from a transform coder. Furthermore, there is also a need to provide an improved frequency-domain correlation method for transform coded complex frequency-domain signals which only comprises the real part or the imaginary part in the bin coefficient. SUMMARY

[0010] It is an object of the invention to address at least some of the problems and issues outlined above. It is an object of embodiments of the invention to determine the absent real or imaginary part of bin coefficient of a complex frequency domain signal which is output from a transform coder. It is another object of embodiments of the invention to provide an improved frequency-domain correlation method for transform coded complex frequency-domain signals which only comprises the real part or the imaginary part in the bin coefficient. It is possible to achieve one or more of these objects and possibly others by using methods and control units as defined in the attached independent claims.

[0011] According to an embodiment, a method for determining a second part of a bin coefficient of a first complex frequency-domain signal is disclosed. A first time-domain signal comprises overlapping input frames and is processed with a Fourier-related transform to provide the first complex frequency-domain signal, the first complex frequency-domain signal is made up of output frames, each outputframe comprises a plurality of bins, each bin being a sub-frequency range within a frequency range of its output frame, and each bin comprises a complex bin coefficient representing the first complex frequency-domain signal in the corresponding bin, wherein only a first part of a real part and an imaginary part of the complex bin coefficient is included in each bin coefficient of the first complex frequency-domain signal, wherein a second part of the real part and the imaginary part of the complex bin coefficient is absent from each bin coefficient of the first complex frequency-domain signal, the method being performed by a control unit , the method comprising the steps of: receiving the first complex frequency-domain signal ; determining the absent second part of each bin coefficient of the first frequency-domain signal based on the first part of the complex coefficient of adjacent bins of the bin being determined; adding, for each bin of the first complex frequency-domain signal, the determined second part to each bin coefficient, so that each bin coefficient of the first complex frequency-domain signal comprises both the real and the imaginary part.

[0012] According to another embodiment, a control unit for determining a second part of a bin coefficient of a first complex frequency-domain signal is disclosed. A first time-domain signal comprises overlapping input frames and is processed with a Fourier-related transform to provide the first complex frequency- domain signal, the first complex frequency-domain signal is made up of output frames, each output frame comprises a plurality of bins, each bin being a sub- frequency range within a frequency range of its output frame, and each bin comprises a complex bin coefficient representing the first complex frequency- domain signal in the corresponding bin, wherein only a first part of a real part and an imaginary part of the complex bin coefficient is included in each bin coefficient of the first complex frequency-domain signal, wherein a second part of the real part and the imaginary part of the complex bin coefficient is absent from each bin coefficient of the first complex frequency-domain signal, the control unit is operative for: receiving the first complex frequency-domain signal; determining the absent second part of each bin coefficient of the first frequency-domain signal based on the first part of the complex coefficient of adjacent bins of the bin being determined; adding, for each bin of the first complex frequency-domain signal, thedetermined second part to each bin coefficient, so that each bin coefficient of the first complex frequency-domain signal comprises both the real and the imaginary part.

[0013] According to other aspects, computer programs and carriers are also provided, the details of which will be described in the claims and the detailed description.

[0014] Further possible features and benefits of this solution will become apparent from the detailed description below. BRIEF DESCRIPTION OF DRAWINGS

[0015] The solution will now be described in more detail by means of exemplary embodiments and with reference to the accompanying drawings, in which:

[0016] Fig.1 is a schematic diagram illustrating an environment in which the embodiments of the present invention may be used.

[0017] Fig.2 is a schematic block diagram illustrating a reception point, according to possible embodiments.

[0018] Fig.3 is a flow illustrating the method performed by a control unit, according to possible embodiments.

[0019] Fig.4 is a schematic diagram illustrating a same-transform correlation between a signal and reference, according to possible embodiments.

[0020] Fig.5 shows examples of impulse response and noise level when sending complex coefficients and for different alternatives, according to possible embodiments.

[0021] Fig.6 is a schematic block diagram illustrating the control unit in detail, according to possible embodiments.DETAILED DESCRIPTION

[0022] Fig.1 is a schematic diagram illustrating an environment in which the embodiments of the present invention may be used. A single source 2 transmits a wireless signal that is received by a plurality of antennas 5a, 5b. The single source 2 does not need to be the only source of signals, but from the perspective of receiving a wireless signal, the single source 2 is the only source of a particular wireless signal that is received by the plurality of antennas 5a, 5b. The single source 2 can be implemented as an instance of user equipment (UE), and can be, for example, what today are commonly known as a mobile phone, smart phone or a tablet / laptop with wireless connectivity. It can also be any other kind of signal source which generates wireless signals that are transmitted to the antennas 5a, 5b.

[0023] The wireless transmission can occur over a cellular communication network that can comply with any one or a combination of 6G, 5G NR (New Radio), LTE (Long Term Evolution), LTE Advanced, W-CDMA (Wideband Code Division Multiplex), EDGE (Enhanced Data Rates for GSM (Global System for Mobile communication) Evolution), GPRS (General Packet Radio Service), CDMA2000 (Code Division Multiple Access 2000), or any other current or future wireless network, as long as the principles described hereinafter are applicable.

[0024] While Fig.1 is illustrated with two antennas 5a, 5b, the embodiments presented herein can be applied with any number of antennas, e.g., one antenna, multiple antennas. The antennas 5a, 5b are provided physically separated. The antennas 5a, 5b can be provided on the same device, on different devices in one location and / or in different locations.

[0025] Each one of the antennas 5a, 5b is connected to a respective reception point 3a, 3b. The antennas 5a, 5b receive the wireless signals and provide these as respective time-domain signals 7a, 7b, to each one of the reception points 3a, 3b. Each one of the reception points 3a, 3b performs a Fourier-related transform to transform the time-domain signals 7a, 7b to respective frequency-domain signal6a, 6b. The frequency-domain signals 6a, 6b are complex signals which only comprise the real part or the imaginary part in the bin coefficients.

[0026] As explained in more detail below, the control unit 1 determines the absent part of the bin coefficients of the complex frequency-domain signals 6a, 6b. Furthermore, the control unit 1 determines a cross-correlation between the complex frequency-domain signals 6a, 6b. The determined cross-correlation can be used to determine phase difference, time difference, power ratio, etc. between the complex frequency-domain signals 6a, 6b. The phase difference, time difference, power ratio, etc. can be used for positioning the single source 2.

[0027] Fig.2 is a schematic block diagram illustrating a reception point 3, according to possible embodiments. The reception point 3 can be either 3a or 3b in the fig.1.

[0028] Fig.2 shows an example of a transform coding of a time-domain signal 7 in a reception point 3. The time-domain signal 7 corresponds to the time-domain signals 7a, 7b in fig.1. The input time-domain signal 7 of the transform coding can be e.g., IQ samples for a single carrier, or for multiple frequency-multiplexed carriers. Input framing creates overlap between each transform block, typically 50%. Here, a(n) and W*(k) are time- and frequency domain windows, which may be complex. DFT is the Discrete Fourier Transform, typically implemented using a Fast Fourier Transform (FFT). The imaginary part of the DFT transform is typically discarded during, or after, multiplication with the frequency-domain window W*(k), where k is the frequency bin index. Discarding of the imaginary part is done to be able to achieve data compression, compensating for the 50% overlap on the input. For practical use of transform coding, a quantization step at the output can also be used for bitrate reduction. Another way for bitrate reduction can be to only send coefficients for bins whose frequency are within the bandwidth of the signals of interest, e.g., configured carriers within a band. Errors due to quantization can be modeled as noise. Alternatively, the real part is discarded. A complex frequency- domain signal 6 is outputted from the reception point 3 and corresponds to the frequency-domain signals 6a, 6b which are respectively outputted from thereception point 3a, 3b, as shown in the fig.1. The complex frequency-domain signal only comprises the real part or the imaginary part in bin coefficient.

[0029] The transform coding can be done as in the following formulas:^^^^(^^^^) = ^^^^^^^^[^^^^(^^^^)], where^^^^(^^^^) = ^^^^∗(^^^^)^^^^^^^^^^^^{^^^^(^^^^)^^^^(^^^^)} = ^^^^∗(^^^^)^^^^^^^^^^^^{ℎ^^^^(^^^^)^^^^∗(^^^^)^^^^(^^^^)} and

[0030] Here, N is the transform size and M is the number of samples between the start of two adjacent transforms which is usually half the transform size. Typically, ℎ^^^^(^^^^) is a smooth window, such as Kaiser-Bessel-derived, or a Kaiser window, having low sidelobe levels in its spectrum, while not too wide main lobe.Common values of ^^^^ include ^^^^ = 12± ^^^^ ^^^^2,^^^^ ∈ ℤ where setting ^^^^ as an even integer,e.g., zero, will have coefficients for positive frequencies in the first half of the spectrum while an odd integer will swap the left and right halves of the spectrum to get same frequency order as when the signal is upconverted to radio frequency.

[0031] A transform decoding, or inverse transform, can be performed afterwards, transforming a frequency-domain signal to a time-domain signal. This is not shown in fig.2 and will not be discussed in detail.

[0032] The basic idea of the invention is that the absent real / imaginary part of the complex coefficient of a given bin of the complex frequency-domain signal can be estimated from the existing imaginary / real part of the coefficient of adjacent bins in the same frame. This estimation makes the bin coefficient of the complex frequency-domain signal “complete” with both the real and imaginary part. Then the complex frequency-domain signal with complete bin coefficient can be used for other applications, e.g., correlation between multiple signals.

[0033] Fig.3, in conjunction with fig.1 and fig.2, describes a method for determining a second part of a bin coefficient of a first complex frequency-domain signal 6a, wherein a first time-domain signal 7a comprises overlapping inputframes and is processed with a Fourier-related transform to provide the first complex frequency-domain signal 6a, the first complex frequency-domain signal 6a is made up of output frames, each output frame comprises a plurality of bins, each bin being a sub-frequency range within a frequency range of its output frame, and each bin comprises a complex bin coefficient representing the first complex frequency-domain signal 6a in the corresponding bin, wherein only a first part of a real part and an imaginary part of the complex bin coefficient is included in each bin coefficient of the first complex frequency-domain signal 6a, wherein a second part of the real part and the imaginary part of the complex bin coefficient is absent from each bin coefficient of the first complex frequency-domain signal 6a, the method being performed by a control unit 1, the method comprising the steps of: receiving 302 the first complex frequency-domain signal 6a; determining 304 the absent second part of each bin coefficient of the first frequency-domain signal 6a based on the first part of the complex coefficient of adjacent bins of the bin being determined; adding 306, for each bin of the first complex frequency-domain signal, the determined second part to each bin coefficient, so that each bin coefficient of the first complex frequency-domain signal comprises both the real and the imaginary part.

[0034] As explained above, the first time-domain signal 7a comprises overlapping input frames. The first time-domain signal 7a is processed with a Fourier-related transform in the reception point 3. The Fourier-related transform can be DFT as shown in fig.2, it can also be another kind of Fourier-related transform. The output signal of the Fourier-related transform is the first complex frequency-domain signal 6a. The first complex frequency-domain signal 6a is made up of output frames, each output frame having a frequency range. The frequency range of the output frame comprises a plurality of bins, so that each bin is a sub-frequency range of the frequency range of the output frame. Each bin comprises a complex coefficient representing the first complex frequency-domain signal 6a in corresponding sub-frequency range of the bin. By all the bins with each coefficient, the first complex frequency-domain signal 6a is represented in the frequency-domain. The coefficient of each bin of the first complex frequency- domain signal 6a comprises a first part and a second part. The first part is the partwhich exists in the coefficient of each bin of the first complex frequency-domain signal 6a and it can be either the real part or the imaginary part. The second part is the part which is absent from the coefficient of each bin of the first complex frequency-domain signal 6a. When the first part is the real part, the second part is the imaginary part and vice versa. Although the second part of the bin coefficient is absent, the complex frequency-domain signal 6a is a complete signal for transmission from UE to the base station since the aliasing from absent imaginary part is cancelled by overlap-add in time domain, i.e., the bin coefficient represents the first complex frequency-domain signal 6a in the corresponding sub-frequency range. The bin coefficient is however incomplete for some other purposes, e.g., correlation, which will be discussed in the embodiments below.

[0035] In the receiving step 302, the first complex frequency-domain signal 6a is received by the control unit 1.

[0036] In the determining step 304, for a current bin coefficient, i.e., the coefficient of the bin being determined, the absent second part of the coefficient is determined based on the first part of the coefficient of adjacent bins of the current bin. The adjacent bins refer to the neighbor bins of the current bin in the same output frame which have higher / lower frequency than the current bin. Since the first part of the coefficient of adjacent bins are known, the absent second part of the current bin coefficient of the first complex frequency-domain signal 6a is determined accordingly. The absent second part of the coefficient is determined for each bin in this way. The determining of the absent second part of bin coefficient based on the first parts of adjacent bin coefficients does not necessarily mean that an empty memory position is to be filled with the determined value. Instead, e.g., a reference to the first parts of the adjacent bin coefficients could be used.

[0037] In the adding step 206, the determined second part is added into the first frequency-domain signal 6a, so that the coefficient of each bin of the first complex frequency-domain signal comprises both the real and the imaginary part.

[0038] By such an embodiment, the absent second part of each bin coefficient is determined based on the existing first part of the coefficients of adjacent bins. Therefore, bin coefficients with both real and imaginary part are obtained, so that the first complex frequency-domain signal becomes more accurate and applicable for other applications, e.g., calculating correlation in frequency-domain.

[0039] A further advantage is that this embodiment can be applied to a stored complex frequency-domain signal so that only the first part needs to be stored and / or that only the first part has to be calculated in the transform coding process. The second part can be determined later on according to the method in this embodiment. By storing and / or calculating only the first part, and determining the absent second part, the data compression rate is improved, with 50% reduction of memory requirements. Furthermore, when the reference to the first parts of the adjacent bin coefficients is used to represent the determined second part of the current bin coefficient, the memory is further saved, since the determined value of the second part does not need to be saved in the memory.

[0040] According to another embodiment, wherein the adjacent bins of the bin being determined comprise a previous neighbor bin to the bin being determined and a next neighbor bin to the bin being determined, and wherein the step of determining 304 the absent second part in each bin coefficient comprises determining the absent second part in each bin coefficient of the first complex frequency-domain signal 6a by, for each bin coefficient, linearly combining the first part of the bin coefficient of the previous neighbor bin and the first part of the bin coefficient of the next neighbor bin of the first complex frequency-domain signals 6a with a respective weight factor.

[0041] In this embodiment, a specific way of determining the absent second part is defined. The previous neighbor bin refers to a neighbor bin of the current bin which has a lower frequency range, and the next neighbor bin refers to a neighbor bin of the current bin which has a higher frequency range. Alternatively, the previous neighbor bin refers to a neighbor bin of the current bin which has a higher frequency range, and the next neighbor bin refers to a neighbor bin of the current bin which has a lower frequency range. The first part of the bin coefficient of theadjacent bins are linearly combined with respective weight factor so as to obtain the absent second part of the coefficient of the current bin. The absolute value of the sum of the two weight factors can be 1. It is possible that one weight factor is 1 and the other weight factor is 0, so that the absent second part is determined only based on the first part of the coefficient of only one adjacent bin. The two weight factors can be equal, e.g.0,5. In a preferred embodiment, the sum is zero since the two weight factors have the same magnitude but opposite signs.

[0042] According to another embodiment, wherein a second complex frequency- domain signal 6b, 6c is processed according to the above embodiment, the method further comprises the step of: determining 308 a cross-correlation between the first complex frequency-domain signal 6a and the second complex frequency- domain signal 6b, 6c by cross-correlating the first complex frequency-domain signal with the added 306 second part in each bin coefficient and the second complex frequency-domain signal with the added 306 second part in each bin coefficient.

[0043] In this embodiment, a second complex frequency-domain signal 6b, 6c is introduced. Similar to the first time-domain signal 7a, a second time-domain signal 7b, 7c comprises overlapping input frames and is processed with a Fourier-related transform to provide the second complex frequency-domain signal 6b, 6c, the second complex frequency-domain signal 6b, 6c is made up of output frames, each output frame comprises a plurality of bins, each bin being a sub-frequency range within a frequency range of its output frame, and each bin comprises a complex bin coefficient representing the second complex frequency-domain signal 6b, 6c in the corresponding sub-frequency range, wherein only a first part of a real part and an imaginary part of the complex bin coefficient is included in each bin coefficient of the second complex frequency-domain signal 6b, 6c, wherein a second part of the real part and the imaginary part of the complex bin coefficient is absent from each bin coefficient of the second complex frequency-domain signal 6b, 6c. The control unit 1 receives the second complex frequency-domain signal 6b, 6c; determines the absent second part of each bin coefficient of the second frequency-domain signal 6b, 6c based on the first part of the complex coefficient ofadjacent bins of the bin being determined; adds, for each bin of the second complex frequency-domain signal, the determined second part to each bin coefficient, so that each bin coefficient of the second complex frequency-domain signal comprises both the real and the imaginary part.

[0044] A cross-correlation between the first complex frequency-domain signal 6a and the second complex frequency-domain signal 6b, 6c can be performed by cross-correlating the first and second complex frequency-domain signals with the added second part of each bin coefficient respectively. The bin coefficients of the first and second frequency-domain signals comprise both the real and imaginary part respectively. Alternatively, the bin coefficient of one frequency-domain signal comprises only real or imaginary part, and the bin coefficient of the other frequency-domain signal comprises both the real and imaginary part.

[0045] By such an embodiment, since the bin coefficients of the input signals of the cross-correlation comprise the real and imaginary part, the correlation result also comprises both real and imaginary part. The problem mentioned in the BACKGROUND, i.e., the aliasing in time-domain, does not exist with this embodiment. The correlation between the two signals becomes more accurate. Furthermore, the SNR of this embodiment is superior to the prior art mentioned in the BACKGROUND when the time-domain windowed overlap area between adjacent transforms is small, e.g., when the tapering window has a narrow bell- shape and / or when the sample overlap between transforms is small. Furthermore, if the determined second part is represented by a reference to the first parts of adjacent bin coefficients, when determining the correlation, the calculations may be made directly on the first part of the adjacent bin coefficients. The determined second part does not occupy any memory. Therefore, the resource required by the correlation calculation is reduced.

[0046] According to another embodiment, the method further comprises the step of determining 310 a time difference, phase difference, or power ratio, between the first frequency-domain signal 6a and the second frequency-domain signal 6b, 6c based on the determined 306 cross-correlation between the first frequency-domain signal 6a and the second frequency-domain signal 6b, 6c.

[0047] By this embodiment, a time difference, phase difference, or power ratio between the two complex frequency-domain signals are calculated based on the correlation between them.

[0048] According to another embodiment, the method further comprises the step of determining 312 a position of the signal source 2 based on at least one of the time difference, phase difference and power ratio, wherein the first time-domain signal 7a originates from the signal source 2.

[0049] By this embodiment, the position of the signal source 2 is determined.

[0050] According to another embodiment, the second time-domain signal 7b, 7c is a reference signal.

[0051] According to another embodiment, the reference signal 7b, 7c is a measured reference signal 7b originated from the signal source 2 or a known reference signal 7c. The measured reference signal 7b can be e.g., measurements of physical uplink shared channel (PUSCH) signal or unknown signal. The known reference signal 7c is an á priori known signal, aka synthetic reference, e.g., sounding reference signal (SRS) or demodulation reference signal (DMRS). The known reference signal 7c can be generated in the control unit 1 or in some other node, e.g., a baseband processing node.

[0052] According to another embodiment, the method further comprises: determining 314 a power spectral density of the first complex frequency-domain signal with the added 306 second part in each bin coefficient of the first complex frequency-domain signal.

[0053] By this embodiment, the first complex frequency-domain signal with determined bin coefficient having both the real and imaginary part is used to determine a power spectral density (PSD). When determining the PSD, having access to both real and imaginary part avoids fluctuations of power per bin depending on phase of the bin coefficient, and thus requires less averaging to determine the PSD.

[0054] According to another embodiment, the method further comprises scaling 316 a real part of the determined 306 cross-correlation and / or an imaginary part of the determined cross-correlation to optimize time-domain alias cancellation.

[0055] According to another embodiment, the method further comprises: normalizing 318 the determined 306 correlation between the first frequency- domain signal 6a and the second frequency-domain signal 6b, 6c on a bin-by-bin basis.

[0056] According to another embodiment, the method further comprises: determining 320 the absent second part of each bin coefficient of the first complex frequency-domain signal 6a based on the first part of the complex coefficient of a bin in an adjacent frame, the bin having same bin index as the bin being determined ; combining 322 linearly the second part of each bin coefficient of the first complex frequency-domain signal 6a determined 320 based on the first part of the complex coefficient of the bin having same bin index in an adjacent frame and the second part of each bin coefficient of the first complex frequency-domain signal 6a determined 304 based on the first part of the complex coefficient of the adjacent bins, wherein the second part of each bin coefficient determined based on the first part of the complex coefficient of the bin having same bin index in an adjacent frame and the second part of each bin coefficient determined based on the first part of the complex coefficient of the adjacent bins are combined with respective combining coefficients.

[0057] By this embodiment, another alternative of determining the absent second part of bin coefficient is defined: based on the first part of the coefficient of the same bin in an adjacent frame. The bin being determined belongs to a current output frame of the first frequency-domain signal 6a. The adjacent frame refers to the adjacent output frame of the current output frame, i.e., a neighbor frame which is earlier or later in time, of the current output frame. So that there are two ways for determining the absent second part of the current bin coefficient: 1. as discussed in above embodiments, determining the second part of the current bin coefficient based on the first part of the coefficients of adjacent bins; 2. as defined in this embodiment, determining the second part of the current bin coefficient based onthe first part of the coefficient of the same bin in an adjacent frame. The combining step 322 is a linear combination of the determining results of the way 1 and the way 2. The result of way 1 and the result of way 2 have respective combining coefficients when linearly combined.

[0058] By this embodiment, the absent second part of the current bin coefficient can be determined by different ways and the determination result can be combined, so that the accuracy of determination can be improved.

[0059] According to another embodiment the combining coefficients of the linear combination 322 are based on a time-domain tapering window of the Fourier- related transform and / or the amount of overlap in input frames.

[0060] According to another embodiment, a complex cross-correlation in transform spectrum is determined despite only having the real part per bin index k.

[0061] Cross-correlation is done between a received signal and a reference. The definition of complex cross-correlation in frequency domain between signal 1 and reference signal 0 is:Here, the expectation operator ^^^^{. } typically refers to averaging over multipletransforms, i.e., a kind of time average.

[0062] In a system using transform coding, typically only the real values of the signals (X terms) are available. If the real and imaginary parts of the signal have the same statistics, the above formula would give us the real part of the cross-correlation as 2 ∙ ^^^^{^^^^1(^^^^)^^^^0(^^^^)}., but without an estimate of any of the Y terms,the formula does not allow us to determine the imaginary part of the correlation.

[0063] In some cases, the reference can be a known signal, e.g., when a UE is transmitting SRS or DMRS. In other cases, such as for PUSCH data or for some strong unwanted interferer or jammer, one of the received signals can be a measured reference. For the measured reference case, if more than two receivedsignals are available, it is suitable to select one reference signal and correlate all the other signals against the same reference. It is typically an advantage if the reference signal is only a time-delayed and attenuated version of the original transmitted signal, i.e., negligible multipath propagation. It is also good if the reference signal has relatively high signal-to-noise ratio. Both of these conditions may be fulfilled in line-of-sight (LoS) signal propagation. To avoid the need for full channel estimation, simpler selection methods like any of the following could be used: • The reference signal can be selected as the signal with highest received signal power, i.e., high probability of line-of-sight, or • the reference branch can be selected as the branch where the signal has the most concentrated autocorrelation which indicating lack of multi-path. This corresponds to the flattest PSD for the received signal assuming that the PSD of the transmitted signal was flat.

[0064] We assume that the real and imaginary part of ^^^^(^^^^)are uncorrelated and have equal statistics. To simplify analysis, wireless channels are assumed to be additive white Gaussian noise (AWGN) channels, i.e., a line-of-sight channel without any multipath propagation, and thus having a flat frequency response.

[0065] Depending on the duration of the desired signal, and on parameters of the transform coding, multiple transforms may be needed to cover the whole signal. Correlation between same transforms of signal and reference can only cover delay differences up to ± half the transform time duration. Supporting larger delay differences, e.g., same delay-difference range as for time-domain convolution, would require, for each bin index k, a convolution between bin coefficients from the multiple transforms of the received signal and bin coefficients from the multiple transforms of the reference. Performing such convolution over all bin indices of interest still has lower complexity than a full time-domain convolution. However, if the delay range of interest is small compared with the duration or input length of a transform, e.g., in an indoor environment if the transform duration is at least a few microseconds, the computational complexitycan be reduced further by only calculating the zeroth lag result of the convolution for each bin index. This means element-wise multiplication between same transform numbers in the received signal and in the reference, i.e., same- transform or same-frame correlation, followed by averaging over the number of transforms. For example, the coefficient of bin index k in transform m of received signal 1 is multiplied with the complex conjugate of the coefficient of bin index k in transform m of the reference. Then, the same operation is done for transform m+1, m+2 and so on, followed by averaging of the result over the number of transforms. Here it is assumed that transform m of received signal 1 is aligned in time with transform m of the reference.

[0066] Fig 4. illustrates same-transform correlation when delay difference is much shorter than transform time. The signal, which is an OFDM symbol here, is longer than the transform time and therefore multiple transforms are used to cover it. It is desired to correlate the shaded parts of Rx and REF for transform m but due to delay difference, a small part of the shaded area for Rx extends into the next interval.

[0067] Fig.4 shows an example of same-transform correlation between a signal Rx and reference REF. The thick curve in fig.4 illustrates the transform’s analysis window. Note that each transform spans two intervals due to the previously mentioned 50% overlap between input frames. Ideally, the same part of Rx and REF should be used in correlation, as shown by the shaded area, but due to delay difference between signal and reference there will be some mismatch. Here, the mismatch is small since the delay difference is small compared with the transform time. Thus, same-transform correlation should give accurate results.

[0068] If needed, e.g., for further analysis, the result of the correlation can then be transformed to time-domain via e.g., an inverse FFT to get a kind an impulse response with one or more peaks corresponding to delay differences between signal and reference. Further, some time-domain windowing can optionally be applied, to correct magnitude and phase, compensating for the impact of the analysis window a(n) in the transform coding. Effectively, the correlation operation in transform frequency domain results in that the time-domain impulse response ismultiplied by the autocorrelation of a(n), slightly distorting magnitude and phase, differently for different delays. If only the delay difference between signal and reference is of interest, or if some magnitude / phase error can be tolerated, this might not matter. However, if accurate magnitude ratio and / or phase difference is important, a time-domain window can be calculated and applied, to compensate, as long as a(n) is known.

[0069] For large delay-differences, it may be necessary to also calculate correlation for other than the zeroth lag between transforms, e.g., Rx transform m+1 correlated with REF transform m, and so on. Then, correlations for different lags must be combined properly in time-domain, e.g., time-shifting, windowing, and summing, to get a longer impulse response.

[0070] The time delay estimates in the transform / time domain are based on the time signals at the reception points 3a and 3b, in Fig.1, here denoted by 0 and 1 respectively, before the DFT in Fig.2, assuming line-of-sight propagation: ^^^^0,^^^^(^^^^0) = ^^^^(^^^^0) ∙ ^^^^0 ∙ ^^^^(^^^^ ∙ ^^^^ + ^^^^0 − ^^^^0)where ^^^^0and ^^^^1are complex amplitudes of the received signals, ^^^^0and ^^^^1are the signal delays, ^^^^ is the transform (or frame) number, M is the number of samplesbetween start of two adjacent frames. Further, , since= ^^^^(^^^^) and weassume that ^^^^(^^^^)^^^^∗(k) = |^^^^(^^^^)|2 = 1 holds for the frequency domain windowW*(k) in Fig.2, at least for the set of transform bins k where we have desired signal. Thus, the frequency domain window will disappear in the correlation formulas below.

[0071] We first derive the correlation between the complex signals in the transform domain.where k is the bin index, ^^^^ = ^^^^1 − ^^^^0 and ^^^^^^^^(^^^^) = ^^^^{^^^^(^^^^ + ^^^^)^^^^∗(^^^^)}, since weassume time-independent auto correlation of ^^^^(^^^^).Changing one summation variable to be ^^^^ = (^^^^1 − ^^^^0 − ^^^^) gives

[0072] In the last step we have used that the window ^^^^(^^^^) = ℎ^^^^(^^^^) ⋅ ^^^^∗(^^^^),where ^^^^ ^^^^ = ^^^^^^^^^ () ^^^ ^^^^^^^^ if ^^^^ = 0 (no swapping of spectrum halves). Typically, ℎ^^^^(^^^^) is asmooth (tapering) window, such as Kaiser-Bessel-derived, or a Kaiser window, having low sidelobe levels while not too wide main lobe.

[0073] Inserting the time correlation for ℎ^^^^(^^^^0) as ^^^^ℎ^^^^(^^^^) = ∑^^^^0 ℎ^^^^(^^^^0 + ^^^^) ∙ℎ^^^^(^^^^0)givesUsinggivesand after breaking out the dependency of ^^^^ we get ^^^^ (^^^^)

[0074] We now use double length for the DFT, ^^^^2 = 2 ∙ ^^^^, since the length of thetime data is essentially doubled, due to the correlation expression ^^^^ℎ^^^^(^^^^):where we only use odd ^^^^1 = 2^^^^ + 1, but for the analysis we may need all ^^^^1.The sum is a DFT of the product ^^^ℎ^ ^^^^(^^^^ + ^^^^) ⋅ ^^^^^^^^(^^^^), which corresponds to aconvolution in the frequency-domain

[0075] Since ^^^^^^^^(^^^^1) is slowly varying in the passband and ^^^^ℎ^^^^(^^^^+^^^^)(^^^^1)essentially is concentrated around ^^^^1 = 0, we might use the approximationWe get the correlation from only the real parts of the frequency data for transform m assince X and Y are assumed uncorrelated and having the same statistics, wherein that X and Y are respectively real and imaginary parts.

[0076] Using the approximation for ^^^^^^^^10(^^^^) above, we get the following:which can be approximated asrespectively, where we also included the approximation from above. If relative magnitude between signal 1 and the reference is of interest, one can compute the normalized correlation by dividing with the power per bin for the reference and by the power of the tapering window (autocorrelation at zero lag).where ^^^^ (^^^^) =is the normalized autocorrelation of ℎ^^^^(^^^^)

[0077] It is proposed to use the first part of coefficients of adjacent bins to determine the absent second part of current bin coefficient of the complex frequency domain signal. Here it is assumed that the spectrum of the signal ^^^^(^^^^)has negligible frequency-domain autocorrelation for frequency shifts corresponding to integer multiples of the transform bin resolution (i.e., frequency distance between adjacent bins). This should be valid in many cases of practical interest, e.g., when the signal s is an OFDM signal with random or scrambled data and the bin resolution of the transform coding is an integer multiple of the subcarrier spacing, or much larger than the subcarrier spacing. Thus, any significant correlation between adjacent bins should be caused by the spectrum of the analysis window ^^^^(^^^^) while the phase of the correlation depends mainly on the frequency-domain window ^^^^∗(^^^^).

[0078] The encoder as shown in Fig.2 may internally generate a complex- valued result, ^^^^(^^^^) = ^^^^(^^^^) + ^^^^^^^^(^^^^),but as mentioned, typically only the real part ^^^^(^^^^)is kept, to allow data compression. For simplicity in the following analysis, we assume that the transmitted signal from the UE has a flat signal spectrum for the set ^^^^ of transform bins that are inside the signal bandwidth with sufficient distance from the signal edge. The signal spectrum is of course not flat for comb-spectrum signals like SRS, but the flat-spectrum assumption might still be valid in the transform spectrum, e.g., when the transform frequency resolution is an integer multiple of the signal’s comb separation (integer number of combs per transform spectrum bin). In cases where the assumption is not valid, a more accurate expression could be derived, e.g., based on the actual signal spectrum.

[0079] We denote said set ^^^^ of transform bins as ^^^^ ∈ ^^^^. Further, we assumethat the channel between UE and RP is an ideal line-of-sight channel with nomultipath. The autocorrelation of ^^^^(^^^^)can be written as^^^^^^^^(^^^^1, ^^^^2) = ^^^^{^^^^(^^^^1)^^^^∗(^^^^2)}Assuming wide-sense stationarity of ^^^^^^^^(^^^^1, ^^^^2), ^^^^1,^^^^2 ∈ ^^^^^^^^^^^^(^^^^1, ^^^^2) = ^^^^^^^^(^^^^) = ^^^^{^^^^(^^^^ + ^^^^)^^^^∗(^^^^)} = ^^^^{(^^^^(^^^^ + ^^^^) + ^^^^^^^^(^^^^ + ^^^^))(^^^^(^^^^) − ^^^^^^^^(^^^^))}= ^^^^{^^^^(^^^^ + ^^^^)^^^^(^^^^) + ^^^^(^^^^ + ^^^^)^^^^(^^^^)} + ^^^^^^^^{^^^^(^^^^ + ^^^^)^^^^(^^^^)− ^^^^(^^^^ + ^^^^)^^^^(^^^^)}Based on the transform coding, the autocorrelation can be calculated as ^^^^ (^^^^) = |^^^^|2^^^^^^^^^^^^{|^^^^(^^^)|2} [ ∗( ) ( )] | |2 2 ∗^^^^ ^ ^^^^ ^^^^ ^^^^ + ^^^^ ^^^^ ^^^^ = ^^^^ ^^^^^^^^^^^^{(ℎ^^^^(^^^^)) }^^^^^^^^ (^^^^)Where ^^^^^^^^is the power of ^^^^(^^^^). Using the earlier definedThe autocorrelation of ^^^^∗becomesFurther, for large N, this autocorrelation can be approximated byThus, ^^^^^^^^(^^^^) ≈ ^^^^ ^^^^^^^^ ∙ ^^^^^^^^^^^^(^^^^) ∙ (−^^^^)≈ [^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ℎ^^^^ ^^^^^^^^^^^^ℎ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^ ^^^^ℎ^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^]≈ ^^^^ ∙ |^^^^ (^^^^)| ∙ (−1)^^^^ ∙ (−^^^^)^^^^ = ^^^^ ∙ |^^^ ( )| ^^^^^^^^ ^^^^^^^^ ^^^^ ^^^^^^^^^ ^^^^ ∙ ^^^^where ^^^^^^^^is the power of ^^^^(^^^^), and ^^^^^^^^^^^^(^^^^) is the autocorrelation of ^^^^^^^^(^^^^), which in turn is the DFT of the tapering window ℎ^^^^(^^^^). The (−^^^^)^^^^in the above corresponds to a time-shift of half the DFT size, since the tapering window has the maximum in the center instead of at the first sample. Thus, the complex sign of the correlation becomes ^^^^^^^^and the phase or complex sign changes by +^^^^ for a shift of +1 bin, −^^^^ for a shift of -1 bin, and by -1 for a shift of ±2 bins. If the assumption of a real and symmetric tapering window with maximum in the center does not hold, the phase change could be different, which may affect some derivations below.

[0080] We further define the normalized autocorrelation of ^^^^(^^^^) asThe phase change for a shift (lag) of +1 or -1 bin, means that the real part of the coefficient of an adjacent bin contains information about the imaginary part of the coefficient of the current bin (and vice versa) if the autocorrelation is non-zero for these shifts. The larger the magnitude of the normalized autocorrelation at these shifts, the better, which typically can be translated to that a narrow-shape time- domain tapering window is better than a wide-shape window. Based on this, we could estimate the missing imaginary part ^^^^(^^^^) of a signal or reference from either^^^^(^^^^ − 1) or ^^^^(^^^^ + 1). However, better performance is achieved by using boththose bins. Our estimate of the imaginary part for signal 1 is thereforewhere ^^^^1(^^^^) is the real-valued coefficient for bin index k from signal 1, ^^^^ is a scale factor that can be set e.g., based on the correlation between adjacent bins, while ^^^^ is an error term that depends on other nearby bins, which we treat as noise that can be averaged out in correlation expressions. In this document, it is assumedthat ^^^^^^^^[^^^^^^^^(1)] > 0 and that ^^^^ > 0 unless otherwise noted. However, a personskilled in the art should be able to correct any relevant formulas, e.g., by sign change or by using absolute values where appropriate, for cases when these conditions are not met.

[0081] The results below will be utilized in the following sections to analyze proper scale values for the real and imaginary parts of the complex correlation ^^^^{^^^^0(^^^^)^^^^1(^^^^)} = ^^^^{^^^0^ (^^^^)^^^1^ (^^^^)}^^^^{^^^1^ (^^^^)^^^^0(^^^^)} = −^^^^{^^^^1(^^^^)^^^0^ (^^^^)}=^^^^ ∙ ^^^^^^^^[^^^^^^^^(1)] ∙ ^^^^{^^^1^ (^^^^)^^^^0(^^^^)}Using the estimate of the imaginary part, we can form an estimate of the complex bin coefficient for signal 1 as: ^̂^^^1(^^^^) = ^^^^1(^^^^) + ^^^^^�^^1^ (^^^^)

[0082] With this estimate, the correlation between signal 1 and the reference 0 can be calculated based on the definition of correlation in frequency domain, but the relative scaling between the resulting real and imaginary parts of the correlation needs further attention. Such scale values will be derived in the following sections.

[0083] Correlation estimates where at least one imaginary part is estimated are denoted with a caret (^) above the parameter name as in ^̂^^^^^^^10(^^^^). Further the corresponding correlation estimate after individual scaling of the real and imaginary parts with proper scaling factors to achieve time-domain alias cancellation isAnd if the corresponding normalized correlation is desired, e.g., to get accurate relative magnitude estimates, it can be calculated as^^ ^̂̂^^^^^ ^^^^10(^^^^)^^^^10(^^^^) =^^^^. ^^^^0 ∙ ^^^^^^^^^^^^(0)where ^^^^^^^^0 = 2^^^^^^^^0 is the average power of the reference over bins ^^^^ ∈ ^^^^.

[0084] The following texts list a number of alternatives, but the invention is not limited to those specific alternatives. Performance in terms of precision of e.g., a delay estimate may differ between the methods.

[0085] Alternative 1: The proposed method is applied only to the reference while signal 1 is real-valued. This section analyzes the case when the proposed method is only used on the reference to create a complex-valued reference from a real- valued reference although only the real part is available for the signal while the imaginary part is set to 0. This could be the case if it is desired to minimize computational complexity when a complex reference is not available. It should be noted that although this embodiment has low complexity, it does not necessarily perform worse than other embodiments in all cases. This can depend on SNR and other factors.As seen on the second row of the formula, the real part of the correlation for bin k depends on the coefficients of the signal and of the reference for bin k, while the imaginary part depends on bin k of the signal and bins k-1 and k+1 of the reference. It can be seen that the real part of the result is only half as large as the desiredvalue, ^^^^^^^^[^^^^^^^^10(^^^^)], and does not depend on ^^^^, since the real part of the correlationis only calculated from the real values of transform bins. A proper scale factor for the real part of the correlation is thusIt is clear from the formula that we must have ^^^^0 to get any information aboutthe imaginary part. From the result, a proper scale factor for the imaginary part becomesSetting ^^^^ 1gives ^^^^^^^^^^^^ = ^^^^^^^^^^^^ = 2 but the value of ^^^^ does not impactperformance in this case, as long as the real and imaginary parts are scaled properly. The resulting formula to determine the complex correlation for this case, including proper scaling, becomes

[0086] Alternative 2: The proposed method is applied to signal 1, while a complex reference is available. This section analyzes the case when the proposed method is only used for signal 1 while a complex-valued synthetic reference is available. Using the definition of complex cross-correlation in frequency domain and our estimate of the imaginary part for signal 1, the correlation between signal 1 (as determined from the proposed method) and a complex reference signal 0 becomesAs seen on the third row of the formula, the real part of the correlation for bin k is based on correlation of the real part of the signal for bin k, ^^^^1(^^^^), with the real part of the reference for bin k, ^^^^0(^^^^), but also on correlation of the real part of thesignal from adjacent bins k-1 and k+1, ^^^^1(^^^^ − 1) and ^^^^1(^^^^ + 1), with the imaginarypart of the reference for bin k, ^^^0^ (^^^^). Further, the fourth row shows that the imaginary part of the correlation is based on correlation of the real value of thesignal for adjacent bins, ^^^^1(^^^^ − 1) and ^^^^1(^^^^ + 1), with the real value of thereference for bin k, ^^^^0(^^^^), but also on correlation of the real part of the signal for bin k, ^^^^1(^^^^), with the imaginary part of the reference for bin k, ^^^0^ (^^^^).

[0087] Alternative 2a: In alternative 2a, both the real part and the imaginary part of the cross-correlation are based on the proposed method, using all availableinformation. The real part is calculated from ^^^^�^^^^1(^^^^)^^^^0(^^^^) + ^�^^1^ (^^^^)^^^0^ (^^^^)� and thenwe get the proper scale factor for the real part asIf we set ^^^^ 1in embodiment a, we get ^^^^^^^^^^^^ = 1, i.e., no further scaling ofthe real part is needed.The imaginary part is calculated from ^^^^�^�^^1^ (^^^^)^^^^0(^^^^) − ^^^^1(^^^^)^^^0^ (^^^^)�. A proper scalefactor for the imaginary part is the same as for the real part:Since the scale factors are equal, time-domain alias cancellation will work even without individual scaling of the real and imaginary parts. However, using the above scale factors, or choosing ^^^^ to get unity scale factors as above, is preferred if the result of the correlation is used to determine the relative magnitude between signal 1 and reference 0. The resulting formula for the scaled correlation becomesIf desired, the normalized correlation can then (for any embodiment) be calculated asThe following two alternatives have somewhat lower computational complexity but use less information than alternative 2a and there could be differences in performance.

[0088] Alternative 2b: in the alternative 2b, only the imaginary part of the cross- correlation is based on the proposed method as in embodiment 2a while the real part is calculated as in prior art. Thus, the scale factor for the imaginary part is unchanged while the scale factor for the real part becomes ^^^^^^^^^^^^ = 2,The resulting formula for the scaled correlation becomes:

[0089] Alternative 2c: in the alternative 2c, only the real part is based on the proposed method, calculated as in embodiment 2a, while the imaginary part is calculated from ^^^^{^^^^1(^^^^)^^^0^ (^^^^)}. The proper scale factors for the real and imaginary part are 2 ^^^^^^^^^^^^= 1+ ^^^^ ∙ ^^^^^^^^[^^^^, ^^^^(1)]The resulting formula for the scaled correlation becomes−2^^^^^^^^{^^^^1(^^^^)^^^0^ (^^^^)}

[0090] Alternative 3: The proposed method is applied to both signal 1 and the reference 0. This section analyzes the case when the proposed method is used both for signal 1 and the reference 0. This could be the case e.g., when a measured reference is used, or to reduce memory or processing requirement for a synthetic reference, storing and / or calculating only the real values. Some performance degradation might happen compared with the case when a complex- valued reference exists. For this case, we have the correlation formula∙ ^^^^^^^^[^^^^^^^^10(^^^^)](^^^^ ∙ ^^^^^^^^[^^^^^^^^(1)])As seen in the formula, the real part of the correlation for bin k is based oncorrelation of the real part of the signal for bins k-1 and k+1, ^^^^1(^^^^ − 1) and^^^^1(^^^^ + 1), with the real part of the reference for bins k-1 and k+1, ^^^^0(^^^^ − 1) and^^^^0(^^^^ + 1).

[0091] Alternative 3a: in alternative 3a, both the real part and the imaginary part of the cross-correlation are based on the proposed method. A proper scale factor for the real part of the correlation is thusIf we set ^^^^ =� 2^^^^^^^^[1−^^^^^^^^(2)], we get ^^^^^^^^^^^^ = 1, i.e., no further scaling of the real part isneeded. A proper scale factor for the imaginary part of the correlation is 1 ^^^^^^^^^^^^= ^^^^ ∙ ^^^^^^^^[^^^^^^^^(1)]As can be seen, setting ^^^^ =gives ^^^^^^^^^^^^ = 1. Thus, there is no ^^^^ thatsimultaneously gives unity scale factor for both the real and imaginary part. The resulting formula for the scaled correlation becomes

[0092] Alternative 3b: in the alternative 3b, only the imaginary part of the cross- correlation is based on the proposed method while the real part is calculated as in prior art. Thus, the scale factor for the imaginary part is unchanged while the scale factor for the real part becomes ^^^^^^^^^^^^ = 2,The resulting formula for the scaled correlation becomes:

[0093] For numerical results of this proposed method, some Monte Carlo simulation results will be shown for a 100 MHz wide 5G NR carrier with 30 kHz subcarrier spacing. For the transform coding, we have N=1024, M=512, and the sample rate is 122.88 MHz. We use one slot, i.e., 14 OFDM symbols, for the correlation calculations. The time-domain tapering window is a Kaiser window with β = 9. SNR for signal 0 and 1 are set to 15 and 0 dB respectively. Signal 0 is selected as the measured reference signal.

[0094] In the first evaluation, we compare noise level in the time-domain impulse response for different embodiments, with the corresponding noise level for a case where both real and imaginary parts of the transform coding coefficients are sent from the reception points. Signal 1 is time shifted relative to signal 0 by -30 samples.

[0095] Fig.5 shows magnitude of the impulse response for different embodiments. For delays near zero samples, the noise level is very similar between alternatives, although some embodiments have a small image spur caused by a slight imbalance between real and imaginary parts before IFFT, which might indicate that the scaling of real and imaginary parts have to be fine-tuned. The spur magnitude is largest for alternatives 1 and 3b. For large delay, either positive or negative, sending both real and imaginary parts from the RP have the lowest noise level but alternatives 2a and 3a are only a few dB worse. Further, alternative 1 has the highest noise levels and the lowest implementation complexity, followed by alternatives 2b and 3b, which have somewhat lower noise levels.

[0096] In the second evaluation, precision of time-difference estimates is studied. Again, signal 0 is selected as the reference signal. Here, signal 1 is time shifted relative to signal 0, uniformly in the range θ=[-4040] samples. Correlation calculations are done according to the case where the proposed method is applied to both signal 1 and reference 0. After determining the frequency-domain cross- correlation using embodiment 3b, a rectangular window is applied on the used bins and the windowed complex cross-correlation is transformed back to time domain using IDFT with oversampling to improve peak localization accuracy. Then peaks are located using interpolation. Synchronization errors are not modeled.

[0097] Repeating the above Monte-Carlo simulation over 200 iterations, the result is the following table where delay error is converted to distance error in meters. The proposed method is compared with a scheme using time-domain cross-correlation of individually decoded transform coded data streams, a scheme where the reception point sends both the real and imaginary part over the fronthaul. As can be seen, all methods have close to zero mean in the estimates.The standard deviation of the distance error is only slightly larger than for the time- domain method and the method where the RP sends both real and imaginary part. The standard deviation of the error for the proposed method is in this case around 1 / 8th of the standard deviation of the error for the method in prior art, i.e., ~18 dB better.

[0098] It should be noted that using e.g., a Kaiser window with very low β, the performance of the method from prior art will improve significantly and for Kaiser β < 3, it may become better than the proposed method. The threshold when this happens can be determined empirically, or based on noise level in the imaginary part, which depends on the circular autocorrelation properties of the tapering window. If the tapering window is not fixed, it may in some cases be desirable to alternate between the proposed method and the prior art method based on which one gives best performance for a given tapering window.

[0099] In practice, it is expected that reception point synchronization errors and delay spread from multipath wireless propagation will dominate the distance- estimate error. Thus, distance errors will be significantly larger than the ones in the table below. Time- Complex Method Alternative domain cross- from prior 3b cross- correlation art correlation in after transform inverse domain. transform Real & (much imag. part higher sent from complexity) RPs (double fronthaul data rate).Distance- Mean -0.001 -0.001 +0.003 -0.001 estimate Standard 0.011 0.011 0.107 0.013 error deviation (m) [000100] According to another embodiment, a control unit 1 for determining a second part of a bin coefficient of a first complex frequency-domain signal 6a is disclosed. A first time-domain signal 7a comprises overlapping input frames and is processed with a Fourier-related transform to provide the first complex frequency- domain signal 6a, the first complex frequency-domain signal 6a is made up of output frames, each output frame comprises a plurality of bins, each bin being a sub-frequency range within a frequency range of its output frame, and each bin comprises a complex bin coefficient representing the first complex frequency- domain signal 6a in the corresponding bin, wherein only a first part of a real part and an imaginary part of the complex bin coefficient is included in each bin coefficient of the first complex frequency-domain signal 6a, wherein a second part of the real part and the imaginary part of the complex bin coefficient is absent from each bin coefficient of the first complex frequency-domain signal 6a, the control unit 1 is operative for: receiving the first complex frequency-domain signal 6a; determining the absent second part of each bin coefficient of the first frequency- domain signal 6a based on the first part of the complex coefficient of adjacent bins of the bin being determined; adding, for each bin of the first complex frequency- domain signal, the determined second part to each bin coefficient, so that each bin coefficient of the first complex frequency-domain signal comprises both the real and the imaginary part. [000101] According to another embodiment, the adjacent bins of the bin being determined comprise a previous neighbor bin to the bin being determined and a next neighbor bin to the bin being determined, and wherein the determining of the absent second part in each bin coefficient comprises determining the absent second part in each bin coefficient of the first complex frequency-domain signal 6a by, for each bin coefficient, linearly combining the first part of the bin coefficient ofthe previous neighbor bin and the first part of the bin coefficient of the next neighbor bin of the first complex frequency-domain signals 6a with a respective weight factor. [000102] According to another embodiment, a second complex frequency-domain signal 6b, 6c is processed according to above embodiment, the control unit 1 is further operative for: determining a cross-correlation between the first complex frequency-domain signal 6a and the second complex frequency-domain signal 6b, 6c by cross-correlating the first complex frequency-domain signal with the added second part in each bin coefficient and the second complex frequency-domain signal with the added second part in each bin coefficient. [000103] According to another embodiment, the control unit 1 is further operative for: determining a time difference, phase difference, or power ratio, between the first frequency-domain signal 6a and the second frequency-domain signal 6b, 6c based on the determined cross-correlation between the first frequency-domain signal 6a and the second frequency-domain signal 6b, 6c. [000104] According to another embodiment, the control unit 1 is further operative for: determining a position of a signal source 2 based on at least one of the time difference, phase difference and power ratio, wherein the first time-domain signal 7a originates from the signal source 2. [000105] According to another embodiment, the second time-domain signal 7b, 7c is a reference signal. [000106] According to another embodiment, the reference signal 7b, 7c is a measured reference signal 7b originated from the signal source 2 or a known reference 7c. [000107] According to another embodiment, the control unit 1 is further operative for: determining a power spectral density of the first complex frequency-domain signal with the added second part in each bin coefficient of the first complex frequency-domain signal.[000108] According to another embodiment, the control unit 1 is further operative for: scaling a real part of the determined cross-correlation and / or an imaginary part of the determined cross-correlation to optimize time-domain alias cancellation. [000109] According to another embodiment, the control unit 1 is further operative for: normalizing the determined correlation between the first frequency-domain signal 6a and the second frequency-domain signal 6b, 6c on a bin-by-bin basis. [000110] According to another embodiment, the control unit 1 is further operative for: determining the absent second part of each bin coefficient of the first complex frequency-domain signal 6a based on the first part of the complex coefficient of a bin in an adjacent frame, the bin in the adjacent frame having same index as the bin being determined; combining linearly the second part of each bin coefficient of the first complex frequency-domain signal 6a determined based on the first part of the complex coefficient of the bin having same bin index in the adjacent frame and the second part of each bin coefficient of the first complex frequency-domain signal 6a determined based on the first part of the complex coefficient of the adjacent bins, wherein the second part of each bin coefficient determined based on the first part of the complex coefficient of the bin having same bin index in the adjacent frame and the second part of each bin coefficient determined based on the first part of the complex coefficient of the adjacent bins are combined with respective combining coefficients [000111] According to another embodiment, the combining coefficients of the linear combination are based on time-domain tapering window of the Fourier- related transform and / or the amount of overlap in input frames. [000112] According to other embodiments, referring to fig.6, the control unit 1 may further comprise a communication unit 602, which may be considered to comprise conventional means for communication with external devices, such as a transceiver for transmission and reception of signals. The instructions executable by said processing circuitry 603 may be arranged as a computer program 605 stored e.g. in said memory 604. The processing circuitry 603 and the memory 604may be arranged in a sub-arrangement 601. The sub-arrangement 601 may be a micro-processor and adequate software and storage therefore, a Programmable Logic Device, PLD, or other electronic component(s) / processing circuit(s) configured to perform the methods mentioned above. The processing circuitry 603 may comprise one or more programmable processor, application-specific integrated circuits, field programmable gate arrays or combinations of these adapted to execute instructions. The control unit 1 may also comprise a power supply, e.g., a battery. [000113] The computer program 605 may be arranged such that when its instructions are run in the processing circuitry, they cause the control unit 1 to perform the steps described in any of the described embodiments of the control unit 1 and its method. The computer program 605 may be carried by a computer program product connectable to the processing circuitry 603. The computer program product may be the memory 604, or at least arranged in the memory. The memory 604 may be realized as for example a RAM (Random-access memory), ROM (Read-Only Memory) or an EEPROM (Electrical Erasable Programmable ROM). In some embodiments, a carrier may contain the computer program 605. The carrier may be one of an electronic signal, an optical signal, an electromagnetic signal, a magnetic signal, an electric signal, a radio signal, a microwave signal, or computer readable storage medium. The computer-readable storage medium may be e.g. a CD, DVD or flash memory, from which the program could be downloaded into the memory 604. Alternatively, the computer program may be stored on a server or any other entity to which the control unit 1 has access via the communication unit 602. The computer program 605 may then be downloaded from the server into the memory 604. [000114] Although the description above contains a plurality of specificities, these should not be construed as limiting the scope of the concept described herein but as merely providing illustrations of some exemplifying embodiments of the described concept. It will be appreciated that the scope of the presently described concept fully encompasses other embodiments which may become obvious to those skilled in the art, and that the scope of the presently described concept isaccordingly not to be limited. Reference to an element in the singular is not intended to mean "one and only one" unless explicitly so stated, but rather "one or more." Further, the term “a number of”, such as in “a number of wireless devices” signifies one or more devices. All structural and functional equivalents to the elements of the above-described embodiments that are known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed hereby. Moreover, it is not necessary for an apparatus or method to address each and every problem sought to be solved by the presently described concept, for it to be encompassed hereby. In the exemplary figures, a broken line generally signifies that the feature within the broken line is optional.

Claims

CLAIMS 1. A method for determining a second part of a bin coefficient of a first complex frequency-domain signal (6a), wherein a first time-domain signal (7a) comprises overlapping input frames and is processed with a Fourier-related transform to provide the first complex frequency-domain signal(6a), the first complex frequency-domain signal (6a) is made up of output frames, each output frame comprises a plurality of bins, each bin being a sub-frequency range within a frequency range of its output frame, and each bin comprises a complex bin coefficient representing the first complex frequency-domain signal (6a) in the corresponding bin, wherein only a first part of a real part and an imaginary part of the complex bin coefficient is included in each bin coefficient of the first complex frequency-domain signal (6a), wherein a second part of the real part and the imaginary part of the complex bin coefficient is absent from each bin coefficient of the first complex frequency-domain signal (6a), the method being performed by a control unit (1), the method comprising: receiving (302) the first complex frequency-domain signal (6a); determining (304) the absent second part of each bin coefficient of the first frequency-domain signal (6a) based on the first part of the complex coefficient of adjacent bins of the bin being determined; adding (306), for each bin of the first complex frequency-domain signal, the determined second part to each bin coefficient, so that each bin coefficient of the first complex frequency-domain signal comprises both the real and the imaginary part.

2. The method according to claim 1, wherein the adjacent bins of the bin being determined comprise a previous neighbor bin to the bin being determined and a next neighbor bin to the bin being determined, and wherein the step of determining (304) the absent second part in each bin coefficient comprises determining the absent second part in each bin coefficient of the first complex frequency-domain signal (6a) by, for each bin coefficient, linearly combining the first part of the bin coefficient of the previous neighbor bin and the first part of thebin coefficient of the next neighbor bin of the first complex frequency-domain signals (6a) with a respective weight factor.

3. The method according to claim 1 or 2, wherein a second complex frequency-domain signal (6b, 6c) is processed according to the method of claim 1, the method further comprising the step of: determining (308) a cross-correlation between the first complex frequency-domain signal (6a) and the second complex frequency-domain signal (6b, 6c) by cross-correlating the first complex frequency-domain signal with the added (306) second part in each bin coefficient and the second complex frequency-domain signal with the added (306) second part in each bin coefficient.

4. The method according to claim 3, further comprising the step of: determining (310) a time difference, phase difference, or power ratio, between the first frequency-domain signal (6a) and the second frequency-domain signal (6b, 6c) based on the determined (308) cross-correlation between the first frequency-domain signal (6a) and the second frequency-domain signal (6b, 6c).

5. The method according to claim 4, further comprising the step of: determining (312) a position of a signal source (2) based on at least one of the time difference, phase difference and power ratio, wherein the first time- domain signal (7a) originates from the signal source (2).

6. The method according to any one of the claims 3-5, wherein the second time-domain signal (7b, 7c) is a reference signal.

7. The method according to the claim 6, the reference signal (7b, 7c) is a measured reference signal (7b) originated from the signal source (2) or a known reference signal(7c).

8. The method according to any one of the preceding claims, further comprising the step of:determining (314) a power spectral density of the first complex frequency-domain signal with the added (306) second part in each bin coefficient of the first complex frequency-domain signal.

9. The method according to any one of the claims 3-8, further comprising: scaling (316) a real part of the determined (306) cross-correlation and / or an imaginary part of the determined cross-correlation to optimize time- domain alias cancellation.

10. The method according to any one of the claims 3-9, the method further comprises: normalizing (318) the determined (306) correlation between the first frequency-domain signal (6a) and the second frequency-domain signal (6b, 6c) on a bin-by-bin basis.

11. The method according to any one of the claims 1-10, wherein the method further comprises: determining (320) the absent second part of each bin coefficient of the first complex frequency-domain signal (6a) based on the first part of the complex coefficient of a bin in an adjacent frame, the bin in the adjacent frame having same index as the bin being determined; combining (322) linearly the second part of each bin coefficient of the first complex frequency-domain signal (6a) determined (320) based on the first part of the complex coefficient of the bin having same bin index in the adjacent frame and the second part of each bin coefficient of the first complex frequency- domain signal (6a) determined (304) based on the first part of the complex coefficient of the adjacent bins, wherein the second part of each bin coefficient determined based on the first part of the complex coefficient of the bin having same bin index in the adjacent frame and the second part of each bin coefficient determined based on the first part of the complex coefficient of the adjacent bins are combined with respective combining coefficients.

12. The method as claimed in claim 11, wherein the combining coefficients of the linear combination (322) are based on time-domain tapering window of the Fourier-related transform and / or the amount of overlap in input frames.

13. A control unit (1) for determining a second part of a bin coefficient of a first complex frequency-domain signal (6a), wherein a first time-domain signal (7a) comprises overlapping input frames and is processed with a Fourier-related transform to provide the first complex frequency-domain signal(6a), the first complex frequency-domain signal (6a) is made up of output frames, each output frame comprises a plurality of bins, each bin being a sub-frequency range within a frequency range of its output frame, and each bin comprises a complex bin coefficient representing the first complex frequency-domain signal (6a) in the corresponding bin, wherein only a first part of a real part and an imaginary part of the complex bin coefficient is included in each bin coefficient of the first complex frequency-domain signal (6a), wherein a second part of the real part and the imaginary part of the complex bin coefficient is absent from each bin coefficient of the first complex frequency-domain signal (6a), the control unit (1) is operative for: receiving the first complex frequency-domain signal (6a); determining the absent second part of each bin coefficient of the first frequency-domain signal (6a) based on the first part of the complex coefficient of adjacent bins of the bin being determined, adding, for each bin of the first complex frequency-domain signal, the determined second part to each bin coefficient, so that each bin coefficient of the first complex frequency-domain signal comprises both the real and the imaginary part.

14. The control unit (1) according to claim 13, wherein the adjacent bins of the bin being determined comprise a previous neighbor bin to the bin being determined and a next neighbor bin to the bin being determined, and wherein the determining of the absent second part in each bin coefficient comprisesdetermining the absent second part in each bin coefficient of the first complex frequency-domain signal (6a) by, for each bin coefficient, linearly combining the first part of the bin coefficient of the previous neighbor bin and the first part of the bin coefficient of the next neighbor bin of the first complex frequency-domain signals (6a) with a respective weight factor.

15. The control unit (1) according to claim 13 or 14, wherein a second complex frequency-domain signal (6b, 6c) is processed by the control unit (1) of claim 13, the control unit (1) is further operative for: determining a cross-correlation between the first complex frequency- domain signal (6a) and the second complex frequency-domain signal (6b, 6c) by cross-correlating the first complex frequency-domain signal with the added second part in each bin coefficient and the second complex frequency-domain signal with the added second part in each bin coefficient.

16. The control unit (1) according to claim 15, the control unit (1) is further operative for: determining a time difference, phase difference, or power ratio, between the first frequency-domain signal (6a) and the second frequency-domain signal (6b, 6c) based on the determined cross-correlation between the first frequency-domain signal (6a) and the second frequency-domain signal (6b, 6c).

17. The control unit (1) according to claim 16, the control unit (1) is further operative for: determining a position of a signal source (2) based on at least one of the time difference, phase difference and power ratio, wherein the first time- domain signal (7a) originates from the signal source (2).

18. The control unit (1) according to any one of the claims 15-17, wherein the second time-domain signal (7b, 7c) is a reference signal.

19. The control unit (1) according to claim 18, the reference signal (7b, 7c) is a measured reference signal (7b) originated from the signal source (2) or a known reference (7c).

20. The control unit (1) according to any one of claims 12-19, the control unit (1) is further operative for: determining a power spectral density of the first complex frequency- domain signal with the added second part in each bin coefficient of the first complex frequency-domain signal.

21. The control unit (1) according to any one of the claims 15-20, the control unit (1) is further operative for: scaling a real part of the determined cross-correlation and / or an imaginary part of the determined cross-correlation to optimize time-domain alias cancellation.

22. The control unit (1) according to any one of the claims 15-21, the control unit (1) is further operative for: normalizing the determined correlation between the first frequency- domain signal (6a) and the second frequency-domain signal (6b, 6c) on a bin-by- bin basis.

23. The control unit (1) according to any one of the claims 13-22, wherein the control unit (1) is further operative for: determining the absent second part of each bin coefficient of the first complex frequency-domain signal (6a) based on the first part of the complex coefficient of a bin in an adjacent frame, the bin in the adjacent frame having same index as the bin being determined; combining linearly the second part of each bin coefficient of the first complex frequency-domain signal (6a) determined based on the first part of the complex coefficient of the bin having same bin index in the adjacent frame and the second part of each bin coefficient of the first complex frequency-domain signal (6a) determined based on the first part of the complex coefficient of the adjacentbins, wherein the second part of each bin coefficient determined based on the first part of the complex coefficient of the bin having same bin index in the adjacent frame and the second part of each bin coefficient determined based on the first part of the complex coefficient of the adjacent bins are combined with respective combining coefficients 24. The control unit (1) as claimed in claim 23, wherein the combining coefficients of the linear combination are based on time-domain tapering window of the Fourier-related transform and / or the amount of overlap in input frames.

25. A computer program (605) comprising instructions, which, when executed by a processing circuitry (603) of a control unit (1), for determining a second part of a bin coefficient of a first complex frequency-domain signal (6a), wherein a first time-domain signal (7a) comprises overlapping input frames and is processed with a Fourier-related transform to provide the first complex frequency- domain signal(6a), the first complex frequency-domain signal (6a) is made up of output frames, each output frame comprises a plurality of bins, each bin being a sub-frequency range within a frequency range of its output frame, and each bin comprises a complex bin coefficient representing the first complex frequency- domain signal (6a) in the corresponding bin, wherein only a first part of a real part and an imaginary part of the complex bin coefficient is included in each bin coefficient of the first complex frequency-domain signal (6a), wherein a second part of the real part and the imaginary part of the complex bin coefficient is absent from each bin coefficient of the first complex frequency-domain signal (6a), causes the control unit (1) to perform the steps: receiving the first complex frequency-domain signal (6a); determining the absent second part of each bin coefficient of the first frequency-domain signal (6a) based on the first part of the complex coefficient of adjacent bins of the bin being determined, adding, for each bin of the first complex frequency-domain signal, the determined second part to each bin coefficient, so that each bin coefficient of thefirst complex frequency-domain signal comprises both the real and the imaginary part.

26. A carrier containing the computer program (605) according to claim 25, wherein the carrier is one of an electronic signal, an optical signal, a radio signal, an electric signal, or a computer readable storage medium.

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