FBMC receiver using a method for synchronization in a frequency domain

Abstract

A filter bank multi-carrier (FBMC) receiver implementing a synchronization in the frequency domain. The receiver includes a synchronization module including an error estimator on the sampling instants and, for each subcarrier, an interpolating filter for reconstructing the samples at the accurate sampling instants. A phase-shifter is provided, for each subcarrier, at the output of the interpolating filter, to make a phase compensation. The phase-shifter can be followed by an equalizer in the frequency domain.

Claims

1. A multi-carrier signal receiver configured to receive a multicarrier signal synthesized by a synthesis filter bank, said receiver comprising a sampling section for sampling the multicarrier signal at sampling instants, and an analysis filter bank comprising a plurality of analysis filters for analysing said sampled multicarrier signal, the outputs of the filters being connected to a Fourier transform module providing, for a plurality of subcarriers, samples in the frequency domain, the receiver comprising: processing circuitry configured to provide an error estimation module, receiving said samples for at least one subset of said plurality of subcarriers from the Fourier transform module, and providing an error on the sampling instants; and, for each subcarrier of said plurality of subcarriers: an interpolating filter, receiving the estimation of the error on the sampling instants and interpolating said samples on this subcarrier to provide an interpolated sample at an error-corrected sampling instant.

2. The receiver according to claim 1, wherein the receiver receives the multicarrier signal over a transmission channel and that the error estimation module makes, for each subcarrier of said at least one subset of sub carriers, an estimation of the impulse response of the synthesis filter bank, the transmission channel and the synthesis filter bank, at the frequency of this subcarrier and calculates a metric from the impulse response thus estimated.

3. The receiver according to claim 2, wherein the metric is a quadratic sum of said impulse responses for the subcarriers of said at least one subset, said metric being calculated at three consecutive sampling instants to give three metric values, the error estimation module determining the instant at which a parabolic function, passing through the three metric values at these three instants, reaches its maximum and by deducing therefrom the error on the sampling instants.

4. The receiver according to claim 3, wherein the at least one subset of said plurality of subcarriers consists of subcarriers having the impulse response higher than a predetermined threshold.

5. The receiver according to claim 2, wherein the metric is a correlation of said impulse responses for the subcarriers of said at least one subset, the error estimation module determining the error on the sampling instants from the phase of the correlation result.

6. The receiver according to claim 1, wherein the interpolating filter uses a spline interpolation function, said function being identical for the plurality of subcarriers.

7. The receiver according to claim 1, wherein the interpolating filter uses a Lagrange interpolation polynomial which is identical for the plurality of subcarriers.

8. The receiver according to claim 1, wherein the receiver further comprises an OQAM post-processing module implemented by the processing circuitry and configured to receive the interpolated samples, an OQAM symbol being represented by two consecutive samples of a same subcarrier, the interpolating filter comprising a first module interpolating the real parts of a plurality of successive samples and a second module interpolating the imaginary parts of said plurality of successive samples.

9. The receiver according to claim 1, wherein, for each subcarrier, the interpolating filter is followed by a phase-shift module making a phase compensation of the interpolated samples by means of a multiplication by a phase term exp(j(k)) where (k) is proportional to the frequency of the subcarrier (k) and to the error on the sampling instants.

10. The receiver according to claim 9, wherein, for each subcarrier, the phase-shift module is followed by an equalizer in the frequency domain.

11. The receiver according to claim 1, wherein said multicarrier signal consists of frames, each frame comprising a preamble followed by a useful data packet, the preamble comprising a plurality of pilot symbols on subcarriers, called active subcarriers, of said plurality of subcarriers, each pilot symbol being surrounded by a time and frequency guard ring, the receiver determining the energy received on said active subcarriers and opening a time window when this energy crosses a predetermined threshold, the receiver then determining the beginning of said packet when the energy of the received signal reaches a maximum.

12. The receiver according to claim 1, wherein said multicarrier signal consists of frames, each frame comprising a preamble followed by a useful data packet, the preamble comprising for at least one carrier, a synchronization sequence, the receiver comprising a synchronization module, implemented by the processing circuitry, in the time domain, said synchronization module receiving the samples at the input of the Fourier transform module and making a correlation between the samples input to the Fourier transform module and said synchronization sequence to obtain a correlation peak, and synchronizing the beginning of the Fourier transform from the position of the correlation peak thus obtained.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further characteristics and advantages of the invention will appear upon reading preferential embodiments of the invention, with reference to the appended figures in which:

(2) FIG. 1 represents the structure of a first FBMC transmission/reception system known from the state of the art;

(3) FIG. 2A schematically represents the pre-processing module of the system of FIG. 1;

(4) FIG. 2B schematically represents the post-processing module of the system of FIG. 1;

(5) FIG. 3 represents the structure of a second FBMC transmission/reception system known from the state of the art;

(6) FIG. 4 illustrates the waveform of the signal at the output of the transmitter of FIG. 3;

(7) FIG. 5 illustrates the waveform of the signal at the output of the transmitter of FIG. 3 when a synchronization preamble is provided;

(8) FIG. 6 schematically represents a FBMC receiver using a synchronization method in the frequency domain, according to a first embodiment of the invention;

(9) FIGS. 7A and 7B respectively illustrate the situation of a synchronized receiver and a receiver having a synchronization error;

(10) FIG. 8 represents a metric used in a module of FIG. 6 to determine an error on the sampling instants;

(11) FIG. 9 represents a signal frame received by the FBMC receiver;

(12) FIG. 10 schematically represents a FBMC receiver using a synchronization method in the time and frequency domains, according to a second embodiment of the invention.

DETAILED DISCLOSURE OF PARTICULAR EMBODIMENTS

(13) FIG. 6 represents a FBMC receiver according to one embodiment of the invention. This receiver comprises an analysis filter bank 610 identical to the filter bank 360 of FIG. 3, a synchronization module 620, as well as a post-processing module 630, identical to the post-processing module 380 of FIG. 3.

(14) The FTT module makes the FFT on the fly, that is without prior alignment at the beginning of a data packet.

(15) The synchronization module receives the samples from frequency bins of the FFT module, each bin being associated with a subcarrier. It consequently operates in the frequency domain.

(16) For a given frequency bin, the sample sequence represents a subcarrier signal, a QAM symbol transmitted by the transmitter on the frequency of the subcarrier corresponding to two successive quadrature samples.

(17) The idea underlying the invention is to make an interpolation between successive symbols (at the output of the FFT), after the error has been estimated on the sampling instants.

(18) For this, the synchronization module 620 comprises an error estimator on the sampling instants 621 and, for each subcarrier k, an interpolating filter 622 receiving the error thus estimated, followed by a phase-shift module 626. This phase-shift module can be optionally followed by an equalizer 627.

(19) Thereafter, a given subcarrier k is considered and R.sub.g.sup.k denotes the convolution between the synthesis filter g.sub.k and the corresponding analysis filter.

(20) When the sampling upon reception does not coincide with the instants when the samples are actually received, as a result, there is an error on the values of the successive samples.

(21) FIG. 7A illustrates the situation where the sampling instants coincide with those when the samples are received. More precisely, FIG. 7A represents the function R.sub.g.sup.k for a transmitted sample. The sampling instant t.sub.n herein coincides with the maximum of the function R.sub.g.sup.k. It is noticed that the values of R.sub.g.sup.k are not null at the instants t.sub.n1 and t.sub.n+1. However, it will be noted that these values do not create interference, given that the samples received on the same channel at the instants t.sub.n1 and t.sub.n+1 are purely imaginary if the sample received at the time t.sub.n is real, and conversely. Further, since the values of R.sub.g.sup.k are null at the instants t.sub.n2 and t.sub.n+2, no interference is generated at these instants either.

(22) FIG. 7B illustrates the situation where the receiver makes an error on the sampling instant t.sub.n.

(23) It is noted that the sampling instant t.sub.n does not correspond any longer to the maximum of the function R.sub.g.sup.k and that interference is generated at the instants t.sub.n2 and t.sub.n+2.

(24) The interpolating filter makes an interpolation between successive samples provided by a demultiplexer (not shown). More precisely, the interpolating filter comprises a first interpolation module interpolating the samples on the real axis and a second interpolation module on the quadrature axis. Since the response R.sub.g.sup.k is substantially identical for two successive samples, it can be considered that the interpolation function is the same on both these axes.

(25) The interpolation can be made by means of an interpolation function .sup.k(t), for example a spline function or a Lagrange polynomial function, in a manner known per se. The interpolation function is determined so as to pass through the values of the plurality of samples.

(26) Thus, if y.sub.nv.sup.k, . . . , y.sub.n1.sup.k, y.sub.n.sup.k, y.sub.n+1.sup.k, . . . , y.sub.n+v.sup.k denotes a series of 2v+1 successive samples at the input of the interpolating filter, with v1, this filter can make an interpolation between 2v+1 samples using the Lagrange polynomial:

(27) $\begin{array}{cc}{}^k\left(t\right)=\underset{i=-v}{\overset{+v}{.Math.}}{y}_{n+i}^k\underset{j=-v}{\overset{+v}{.Math.}}\frac{t-t_{n+j}}{t_{n+i}-t_{n+j}}& \left(2\right)\end{array}$
where t.sub.n is the instant associated with the sample y.sub.n.sup.k.

(28) From the error on the sampling instants, the interpolating filter determines for each sample y.sub.n.sup.k, the corrected value:
{tilde over (y)}.sub.n.sup.k=.sup.k(t.sub.n+)(3)

(29) It will be understood that the value {tilde over (y)}.sub.n.sup.k will be either real or imaginary, depending on the parity of n.

(30) It is important to note that the interpolation functions .sup.k are identical for all the subcarriers, in other words:
.sup.k=,k=0, . . . ,N1(4)

(31) Thus, the calculation of the interpolation function will only be able to be made once for all the N subcarriers. Alternatively, the calculation will be able to be made on a set of carriers and the coefficients of the interpolation polynomials will be able to be averaged on this set.

(32) In any case, a series of interpolated samples {tilde over (y)}.sub.n.sup.k is provided at the input of the phase-shift module 626.

(33) The interpolation re-sampling as described above enables the inter-symbol interference to be restricted. The inter-symbol interference rejection will depend on the quality of the interpolating filter.

(34) On the other hand, this re-sampling does not enable to correct the phase error due to the time misalignment of the analysis filter bank with the synthesis filter bank, in other words to compensate for the phase error due to the time misalignment of the impulse response of the analysis filter with respect to that of the corresponding synthesis filter. Thus, for a given subcarrier k, the result of the convolution between the synthesis filter and the analysis filter at the time t.sub.n, in view of (1), is expressed, at the output of the FFT, by:

(35) $\begin{array}{cc}{R}_g^k\left[n\right]=g_k\left[n\right]g_k^{*}\left[n-\right]=g\left[n\right]g^{*}\left[n-\right]\exp \left(j\frac{2k}{M}\right)& \left(5\right)\end{array}$
where =/T denotes the error on the sampling instant expressed in (decimal) number of the sampling period T.

(36) It is noted that, when is an integer multiple of M, the phase term at the right of the expression (5) disappears. In this case, the sampling instants at the receiver correspond to the instants at which the samples transmitted by the transmitter are received.

(37) On the other hand, if the sampling instant is not accurate, a phase ramp

(38) $\left(k\right)=\frac{2k}{M}$
appears on the different subcarriers, at the output of the FFT.

(39) For a given subcarrier k, the interpolated samples {tilde over (y)}.sub.n.sup.k at the input of the phase-shift module 626 are phase-shifted in the phase-shift module 626. More precisely, the phase-shift module makes a phase compensation by means of a multiplication by the phase term exp(j(k)).

(40) Optionally, the phase-shift module can be followed by an equalizer, 627, in the frequency domain. This equalizer can operate on two successive symbols (that is on successive samples having ranks with a same parity) or on a plurality P of successive samples (linear filter with P samplings). The equalizer can implement a ZF (Zero Forcing)- or MMSE (Minimum Mean Square Error)-type equalization method in a manner known per se.

(41) The error estimator on the sampling instants 621 makes an estimation of the impulse response of the synthesis filter bank, channel, analysis filter bank set at the frequency of each subcarrier k, as detailed later.

(42) If the channel spread is low with respect to the duration of the FBMC symbol, the aforesaid impulse response for the subcarrier k can be expressed in the following form:
h.sub.k[n]=.sub.kR.sub.g[n](6)
where R.sub.g[n]=g[n] g[n] is the autocorrelation function of the prototype filter and .sub.k is the channel coefficient at the frequency of the subcarrier k.

(43) The error estimator on the sampling instants, 621, makes the calculation of a metric obtained by quadratically summing the impulse responses relating to the different subcarriers:

(44) $\begin{array}{cc}T\left[n\right]=\underset{k}{.Math.}{.Math.h_k\left[n\right].Math.}^2={.Math.R_g\left[n\right].Math.}^2\underset{k}{.Math.}{.Math.{}_k.Math.}^2& \left(7\right)\end{array}$

(45) This summation can relate to all the subcarriers or can be restricted to those that do not undergo a high fading. Given that the autocorrelation function intervenes identically for all the subcarriers, this amounts to determining the subcarriers k, such that h.sub.k[n]|.sup.2>, where is a predetermined threshold.

(46) It can be shown that the metric T[n] is maximum and reaches the value given by the expression (7) when the error on the sampling instant is null.

(47) The error estimator on the sampling instants 621 calculates the metric T[n] defined by (7) for three consecutive samples, that is T[n1], T[n], and T[n+1] and determines the instant at which this metric reaches its maximum.

(48) To do this, the parabola passing through the points (t.sub.n1,T[n1]), (t.sub.n,T[n]), (t.sub.n+1,T[n+1]) is considered as illustrated in FIG. 8. The maximum of the parabola is reached at the instant t.sub.n+.T such that:

(49) $\begin{array}{cc}=\frac{T\left[n+1\right]-T\left[n-1\right]}{T\left[n+1\right]+T\left[n-1\right]-2T\left[n\right]}& \left(8\right)\end{array}$
where represents the error on the sampling instants, as a fractional number of the sampling period.

(50) Alternatively, the error on the sampling instants can be determined by the estimator 621 from the correlation between impulse responses relating to different subcarriers. If h.sub.k[n] and h.sub.k+m[n] denote the impulse responses of the synthesis filter, channel, analysis filter set, for the subcarriers k and k+m, the correlation between the impulse responses is expressed as:

(51) $\begin{array}{cc}{h}_k\left[n\right]h_{k+m}^{*}\left[n\right]={}_k{}_{k+m}^{*}{.Math.R_g\left[n\right].Math.}^2\exp \left(-2j\frac{m}{M}\right)& \left(9\right)\end{array}$

(52) The error estimator 621 calculates a correlation metric by summing the correlation terms on a plurality of subcarriers, that is:

(53) 0$\begin{array}{cc}{T}^{}\left[n\right]=\underset{k}{.Math.}{h}_k\left[n\right]h_{k+m}^{*}\left[n\right]={.Math.R_g\left[n\right].Math.}^2\exp \left(-2j\frac{m}{M}\right)\underset{k}{.Math.}{}_k{}_{k+m}^{*}& \left(10\right)\end{array}$

(54) When the transmission channel is little or not selective in frequency, that is when .sub.k.sub.k+m, the error can be determined from the phase of T[n].

(55) According to one alternative, if the receiver conducts a channel estimation for the different subcarriers, the coefficients .sub.k are not known. The error can be determined from T[n] and the term

(56) $\underset{k}{.Math.}{}_k{}_{k+m}^{*}.$

(57) In any case, the error estimator 621 should be capable of estimating the impulse response k.sub.k[n]. This impulse response can be obtained from pilot symbols placed for example in the preamble of the useful data packet.

(58) In practice, the impulse response h.sub.k[n] has a time and frequency spread. The prototype filter is chosen such that this spread is relatively low.

(59) For example, as the prototype filter, the filter defined by the following coefficients can be chosen:

(60) $\begin{array}{cc}h\left[n\right]=1+\underset{k=1}{\overset{K-1}{.Math.}}{\left(-1\right)}^{k}H\left(k/L\right)\cos \left(2kn/L\right)\mathrm{for}1nL-1h\left[0\right]=0& \left(11\right)\end{array}$
with K=4; H(1/L)=0.972; H(2/L)=1/{square root over (2)}; H(3/L)=0.235.

(61) In this case, the interference generated by a symbol at time t.sub.n by the subcarrier k can be viewed by means of the table:

(62) TABLE-US-00001 t.sub.n2 t.sub.n1 t.sub.n t.sub.n+1 t.sub.n+2 k 1 0.1250 0.2063j 0.24 0.2063j 0.1250 k 0 0.5638 1 0.5638 0 k + 1 0.1250 0.2063j 0.24 0.2063j 0.1250

(63) It is understood that the interference generated by the symbol in question only extends on two sampling periods before and after said symbol and on a subcarrier on either side of the subcarrier k.

(64) In order to obtain an unbiased estimation of the impulse response h.sub.k[n], a guard ring is advantageously provided around each pilot symbol, in time and frequency.

(65) In the case of the spread indicated above, the guard ring will have a time extent of two sampling periods before and after the pilot symbol and a frequency extent of one subcarrier on either side of the same.

(66) FIG. 9 schematically represents a frame of the signal received by the receiver. This frame comprises a preamble 910, followed by a useful data packet 920. The preamble comprises pilot symbols indicated by black diamonds. The useful data are indicated by grey diamonds (for the imaginary values) and grey circles (for real values).

(67) Alternatively, the pilot symbols can be incorporated within the useful data packet.

(68) It has been seen previously that the receiver synchronization includes, on the one hand, the sampling setting and on the other hand, the determination of the beginning of each useful data packet.

(69) If the frame format of FIG. 9 is used, that is a preamble including pilot symbols on some subcarriers only, called active subcarriers, the beginning of the packet is detected as follows: the energy is calculated on all the active subcarriers; when this energy is higher than a predetermined threshold value, a time window of Q samples is opened from the instant when the threshold is crossed; then, within this window, the instant when the energy maximum of the received signal is reached is searched for, which maximum corresponds substantially to the beginning to the useful packet. n.sub.max denotes the rank of the sample corresponding to the instant when this maximum is reached. To refine the estimation of this instant, the metric values T[n.sub.max], T[n.sub.max1], T[n.sub.max+1] can be calculated and the parabolic interpolation described above can be made. The instant (n.sub.max+)T then gives accurately the instant corresponding to the first sample of the packet. It will be understood that the beginning of the packet and the sampling instant are consequently jointly determined.

(70) FIG. 10 schematically represents a FBMC receiver using a synchronization method in the time and frequency domains, according to a second embodiment of the invention.

(71) As in the first embodiment, the receiver comprises an analysis filter bank 1010, a first synchronization module 1020 operating in the frequency domain and an OQAM post-processing module 1030. The modules 1010, 1020, and 1030 are respectively identical to the modules 610, 620, and 630 of FIG. 6.

(72) Unlike the first embodiment, the FBMC receiver of FIG. 10 comprises a second synchronization module 1040 operating in the time domain, in other words before the FFT.

(73) This embodiment assumes that a synchronization sequence is present in the preamble. On the transmitter side, this synchronization sequence is incorporated in the preamble downstream of the IFFT module, on at least one subcarrier.

(74) On the receiver side, the second synchronization module makes a correlation between the outputs of the analysis filters and the synchronization sequence. The correlation peak enables the beginning of the FFT to be determined. However, since this peak is generally weak and noisy, it is not possible to obtain accurately the sampling instant.

(75) Advantageously, the second synchronization module makes a coarse synchronization and the first synchronization module makes a fine synchronization by means of an interpolation of the samples in the frequency domain as described within the scope of the first embodiment.