a, 1b and 1c are illustrations of known frame constructions of types 1, 2 and 3, respectively, for a system with two send antennas.
a, 5b, and 5c are plots of the real part of the coefficient of the channel as a function of the carrier index.
An estimation method of the invention estimates transmission channels in a multi-antenna system. A transmission channel links a send antenna TXi to a receive antenna RXj. A multi-antenna system uses Nt≧2 send antennas, at least one receive antenna, and a time-frequency frame for each send antenna. A time-frequency frame determines the temporal location of payload data symbols and pilot symbols on the various carriers. The time-frequency frame can further include null symbols, but as these are not involved in the estimation method, they are not referred to in this description. Nor does the description refer to the guard carriers, as they are not involved in the estimation method either. The pilot symbols for the same send antenna form a training sequence. The Nt training sequences are temporally offset from each other within a time interval. They are known to the receiver and enable it to estimate Nt impulse responses that correspond to the Nt transmission channels. The data symbols and pilot symbols are frequency-modulated by an orthogonal multiplexer to form orthogonal symbols that are sent by the send antenna connected to the orthogonal multiplexer in the form of a multi-carrier signal with NFFT carriers including Np pilot carriers and null carriers. Depending on the time-frequency frame concerned, the pilot symbols can be distributed over one or more orthogonal symbols. In one particular embodiment the modulation is OFDM modulation.
An estimation method of the invention is executed in the receiver after a demodulation step which demodulates a time-domain signal received by the receive antenna RXj concerned by means of an FFT of size NFFT to obtain a frequency-domain signal Rj(n) and to extract therefrom Np pilot symbols. In one particular embodiment, the demodulation is OFDM demodulation. The size NFFT of the FFT is typically determined as a function of the size of the inverse FFT applied on sending. These sizes are typically made identical.
The estimation method 1 of the invention includes a step 2 of calculating a matrix A and, for a given receive antenna RXj, a step 3 of calculating the Nt impulse responses in the time domain of the Nt channels linking a send antenna TXi to the respective receive antenna RXj. To obtain the Nr×Nt channels, it is necessary to repeat step 3 for the various receive antennas RXj.
The calculation step 2 calculates a matrix A constructed in the form of blocks from training sequences and a Fourier matrix with dimensions NFFT×NFFT.
The step 3 of calculating the Nt impulse responses in the time domain multiplies the Np pilot symbols with a product of matrices comprising the pseudo-inverse matrix of the product of the Hermitian matrix of the A×A matrix. This multiplication by the product of particular matrices decorrelates the modulated carriers adjacent null carriers.
The transmission system SY includes a multi-carrier sender device EM and a receiver device RE. The sender device EM is connected to Nt send antennas TX1, . . . , TXNt, where Nt≧2. The receiver device RE is connected to Nr receive antennas RX1, . . . , RXNr, where Nr≧1.
In the example shown, the sender device EM includes a channel coder module CdC, a bit interleaver EB, a binary to symbol coding module CBS, a space-time coding module CET, and as many OFDM multiplexers MX as there are send antennas.
The channel coding module CdC codes input source data corresponding to one or more signals, typically telecommunication signals, to supply coded output data dc, for example using a convolutional code.
The bit interleaver interleaves the bits of the coded data in accordance with a particular interleaving law to supply interleaved coded data dce.
The symbol to binary coding module CBS transforms the interleaved coded data dce into complex data symbols sc, for example by BPSK (binary phase-shift keying), QPSK (quadraphase-shift keying) or 16-QAM (quadrature amplitude modulation) modulation.
The space-time coding module CET determines from the complex data symbols sc a two-dimensional matrix of data symbols sd, for example in accordance with an Alamouti-type code, and generates pilot symbols.
Each OFDM multiplexer modulates the data symbols sd and pilot symbols sp inserted at the input of the multiplexer by sinusoidal sub-carriers having orthogonal functions that are the conjugate Fourier components of an inverse Fourier transform of size NFFT corresponding to the number of carriers of an OFDM multiplex. The NFFT carriers comprise Nmod modulated data carriers and Np pilot carriers. The set of NFFT carriers is referred to as an OFDM symbol. The OFDM symbols can include null carriers and guard carriers that are not modulated. The output of an OFDM multiplexer constitutes the time-domain OFDM signal without guard intervals.
Prior to sending, the sender device inserts a guard interval into the OFDM signal.
The signals sent include reference sequences. For each send antenna concerned, a reference sequence is determined by the pilot symbols contained in one or more OFDM symbols. The sequence is determined by the number g of these OFDM symbols, the amplitude of the pilot symbols, and the pilot carriers. The reference sequences are identical to each other but time-shifted relative to each other by an interval Δt least equal to the maximum length L of the transmission channels, Δt≧L, so that the impulse responses of the various channels do not interfere with each other. The time to transmit of a channel or the transmission delay introduced by the channel is referred to as the length of the channel. The interval Δt must be understood as a number of time intervals between samples. The time shift between reference sequences is typically applied before the OFDM modulation by phase-shifting the pilot symbols in the various reference sequences in the frequency domain.
If c(p), p=0, . . . , Np−1 denotes the pilot symbol sent on the carrier frequency of index p at the send antenna TX1, the pilot symbol sent in the same OFDM symbol period at the antenna TXi is equal to:
Moreover, the condition for determining all the impulse responses is Nt×Δt≦Np.
In the example illustrated, the receiver device RE includes as many OFDM demultiplexers DX1, . . . , DXNr as there are receive antennas RX1, . . . , RXNr. It further includes a channel estimation module EsT, an equalization module EgL, a symbol to binary decoding module DbS, a bit de-interleaver Dbt, and a channel decoder module DEC.
Each signal received by a receive antenna is processed by an OFDM demultiplexer. An OFDM demultiplexer applies the function that is the inverse of the function of an OFDM multiplexer. Thus an OFDM demultiplexer applies a direct Fourier transform of size NFFT to the received signal, after elimination of the guard time. An OFDM demultiplexer demodulates a time-domain signal received by the receive antenna RXj concerned by means of an FFT of size NFFT to obtain a frequency-domain signal Rj(n) and extract Np pilot symbols from it.
The outputs of the OFDM demultiplexer supply frequency-domain OFDM signals Rj(n) that are processed by the estimation module and the equalization module.
The signal from the receive antenna RXj can be expressed in the frequency domain at the time n, i.e. after elimination of the guard time and after OFDM demodulation, in the form of a column vector of dimension NFFT:
where X′(n) is a vector of dimension NFFT, the OFDM symbol sent at the time n at the antenna TXj;
F is the Fourier matrix with dimensions NFFT×NFFT;
hj,i(n) is the column vector representing the L samples of the frequency response of the sub-channel linking the send antenna TXi to the receive antenna RXj; and
Ξj(n) is the column vector of dimension NFFT representing the Fourier transform of Gaussian additive white noise.
To simplify the calculations, which is advantageous, the estimation method processes the demodulated signal according to equation (2) only over the period Δt:
F′ is the matrix containing the first Δt columns of the Fourier matrix F with dimensions NFFT×NFFT and h′i,j is a column vector of size Δt such that:
h′j,i=[hj,i
A diagonal matrix having the column vector x on its diagonal is denoted diag{x}:
The Fourier matrix F is a square matrix with dimensions NFFT×NFFT of the following form:
Each OFDM symbol Xi(n) sent at the time n by the send antenna TXi can be broken down into a vector containing the data symbols and a vector containing the pilot symbols:
X
i(n)=Si(n)+Bi(n) (8)
where Si(n) is the vector of the payload data symbols with dimension NFFT and Bi(n) is the vector of the pilot symbols with the same dimension.
Equation (3) can therefore be expressed in the form:
Knowing that Δt≧L, we can impose Δt=L. With this condition, the accumulation of received vectors corresponding to the g orthogonal symbols sent containing pilot symbols constituting a training sequence can be expressed in the form:
where Rj is a column vector of dimension NFFT×g;
T is a matrix with dimensions (NFFT×g)×(Nt×Δt) containing the payload data symbols during the training sequences (of the Nt send antennas);
A is a matrix with dimensions (NFFT×g)×(Nt×Δt) containing the pilot symbols during the training sequences (of the Nt send antennas);
h′j is the column vector of dimension Nt×Δt containing the Nt impulse responses;
h′j=[hj,l
Ξj is the column vector of dimension NFFT×g containing g representations of the Fourier transform of Gaussian additive white noise.
The channel estimation module includes means for calculating the matrix A using equation (12), typically instructions of a program that in a preferred embodiment is incorporated in an electronic circuit, a calculation unit such as a processor or the like whose operation is then controlled by the execution of the program.
To estimate the impulse response vector from the received signal RJ, Barhumi uses the following equation:
ĥj=A+Rj (14)
in which the symbol + signifies the pseudo-inverse. The pseudo-inverse operation is the following operation:
A
+=(AHA)−1AH (15)
To eliminate the interference terms caused by the data symbols present in the OFDM symbol, the product of A+ and T must be equal to a null matrix, which is made possible by imposing non-contiguous sets of pilot symbols and data symbols. Furthermore, calculating the impulse responses can be simplified by considering in the equations only the frequencies dedicated to channel estimation, i.e. by limiting the calculations to the pilot carriers:
ĥj=Ã+{tilde over (R)}j (16)
where {tilde over (R)}j is the matrix with dimensions (Np×g)×1 extracted from Rj considering only the pilot carriers; and
à is the matrix with dimensions (Np×g)×(Nt×Δt);
The estimated value ĥj is therefore a column vector containing the Nt impulse responses. To obtain separately the various frequency responses of the sub-channels necessary for the equalization phase, the method effects vector windowing of the estimated vector ĥj.
If there are null sub-carriers at the edges of the spectrum, the Barhumi solution, equations (14) and (16), leads to edge effects, i.e. to discontinuities at the edges of the spectrum, and this degrades performance.
A solution according to the invention effects an estimate of the impulse responses ĥj using the following equation instead of equation (16):
ĥ
j=(ÃHÃ)+ÃH{tilde over (R)}j (18)
According to this equation, the estimate of the vector of the impulse responses hj is equal to a product of matrices with the received signal {tilde over (R)}j. The product of matrices is equal to the product of the pseudo-inverse matrix of the product of the Hermitian matrix of the à matrix with the à matrix with the Hermitian matrix of Ã.
The multiplication by the pseudo-inverse matrix of the matrices product ÃH×à decorrelates the modulated carrier and null carrier regions.
The channel estimation module includes means for calculating the Nt impulse responses ĥj using equation (18), typically instructions of a program which in a preferred embodiment is incorporated in an electronic circuit, a calculation unit such as a processor or the like of operation that is then controlled by the execution of the program.
Knowing the parameters of the multi-antenna system (the size NFFT of the FFT, the number Nmod of modulated carriers, the time shift Δt between reference sequences, the number g of pilot OFDM symbols forming a reference sequence, and the amplitude c(p) of the pilot symbols), an estimation method and module of the invention advantageously pre-calculate the product of matrices corresponding to the expression:
(ÃHÃ)+ÃH (19)
In a preferred embodiment, the estimation method, respectively the estimation module, multiplies this pre-calculated product of matrices with the demodulated OFDM signal to obtain an estimate of the Nt channels accumulated in the expression for ĥj according to equation (18).
To obtain an estimate of the Nr×Nt channels, the calculation of ĥj must be repeated for j varying from 1 to Nr.
The vector expression for the channel ĥj,i linking the particular send antenna i, for i assuming a value from 1 to Nt, to the particular receive antenna j, for j assuming a value from 1 to Nr, is obtained by making a selection from the Np successive samples of the column vector ĥj calculated for the receive antenna j, starting from the sample (i−1)×Np.
In one particular embodiment of the method, the calculation of the Nt×Nr impulse responses previously described for the Np pilot carriers is completed by an interpolation that can be linear in time or linear in frequency (one-dimensional (1D) interpolation) to obtain the coefficients of each channel for all of the carriers modulated with payload data. The interpolation can be of an order higher than one.
The following two examples illustrate the calculation of the expression for  and, for the first example, also the expression (19): (ÃHÃ)+ÃH.
The parameters of the system take the following values: NFFT=8, Nmod=6, and Δt=2. The unmodulated sub-carriers are assumed to be situated at the two ends of the spectrum. It is assumed that only one OFDM symbol is necessary for estimating the channel (g=1), and the pattern of that OFDM symbol, which constitutes a reference sequence, is represented in Table 2. The first column represents the frequency-domain indices and the second the associated data type (N=null carrier, P=pilot symbol, D=payload data).
The transmission system comprises N2=2 send antennas and Nr=1 receive antenna. Equation (2) gives the expression for the pilot symbol modulating the carrier p for the reference sequence sent by the send antenna TXi, with i=1 or 2:
c(p)1 is therefore the pilot symbol modulating the carrier frequency p for the reference sequence sent by the send antenna TX1 and c(p)2 is the pilot symbol modulating the carrier frequency p for the reference sequence sent by the send antenna TX2.
In the example, c(p)=1 for all the pilot carriers. The vectors of the pilot symbols B1 and B2 and the extracted vectors limited to the pilot carriers {tilde over (B)}1 and {tilde over (B)}2 are then expressed in the form:
The Fourier matrix F is as follows:
in which the symbol j represents the square root of minus one, i.e. the solution of the equation j2=−1. The matrices F′ and {tilde over (F)}′ are expressed in the following form:
The matrix à is then expressed in the following form:
whence the following expressions for ÃH, (ÃHÃ)+ and (ÃHÃ)+ÃH:
The parameters of the system take the following values: NFFT=8, Nmod=6, and Δt=2. The transmission system comprises Nt=3 send antennas and Nr=1 receive antenna. The number of pilot carriers Np=4 is now insufficient because the condition Nt×Δt≦Np is not satisfied. It is therefore necessary for this transmission system to have at the minimum Np=6, for example Np=Nmod=6. The unmodulated sub-carriers are assumed to be situated at the two ends of the spectrum. It is assumed that only one OFDM symbol is needed to estimate the channel (g=1), and the pattern of that OFDM symbol, which constitutes a reference sequence, is represented in Table 3. The first column represents the frequency-domain indices and the second column the associated data type (N=null carrier, P=pilot symbol).
Equation (2) gives the expression for the pilot symbol modulating the carrier p for the reference sequence sent by the send antenna TXi, with i=1, 2 or 3:
c(p)1 is therefore the pilot symbol modulating the carrier frequency p for the reference sequence sent by the send antenna TX1, c(p)2 is the pilot symbol modulating the carrier frequency p for the reference sequence sent by the send antenna TX2, and C(p)3 is the pilot symbol modulating the carrier frequency p for the reference sequence sent by the send antenna TX3.
In the example, c(p)=1 for all the pilot carriers. The vectors of the pilot symbols B1, B2 and B3 and the extracted vectors limited to the pilot carriers, {tilde over (B)}1, {tilde over (B)}2 and {tilde over (B)}3 are then expressed in the form:
The Fourier matrix F is as follows:
in which the symbol j represents the square root of minus one, i.e. the solution of the equation j2=−1. The matrices F′ and {tilde over (F)}′ are expressed in the following form:
The matrix à is then expressed in the following form:
a is a plot of the real part of the coefficient of the channel as a function of the index of the carrier, which varies from 0 to 1023, knowing that the Fourier transform (FFT) has a size of 1024 samples and that the ratio Eb/N0 is equal to 20 dB.
Number | Date | Country | Kind |
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06 53625 | Sep 2006 | FR | national |