Method for decoding linear space-time codes in a multiple-antenna wireless transmission system and decoder therefor

• US 20060050804A1
• Filed: 06/13/2003
• Published: 03/09/2006
• Est. Priority Date: 06/14/2002
• Status: Active Grant

• Current Assignee: ComSIS Co.
• Original Assignee: ComSIS Co.
• Inventors: Leclair, Philippe
• Granted Patent: US 7,330,519 B2
• Time in Patent Office: Days
• US Class Current: 375/267
• CPC Class Codes: H04L 1/0618 Space-time coding

Abstract

An iterative method and a decoder for decoding space-time codes in a communication system with multiple transmission and reception antennae, strikes a compromise between techniques based on interference cancellation algorithms such as BLAST, which show faulty performance concerning error rate based on signal-to-noise ratio and techniques based on maximum likelihood algorithms which are optimal in terms of performance, but highly complex in implantation such as the sphere decoder. Therefor the method includes using a first matrix product between the received signal (Y) and a shaping matrix (B^l), and a second matrix product between a subtraction matrix (D^l) and the vector of the estimated symbols (S^l−1) during the preceding iteration. The estimated symbols during the current iteration are generated by a subtractor (9) receiving the results (r^l,z^l) of the two matrix products. The role of the matrix D^l is to subtract from the current information symbol S^l the interference caused by the other information symbols.

Claims

1. An iterative method for decoding a signal vector Y obtained from N sampled signals in a space-time communication system with M transmission antennae and N receiving antennae, with N greater than or equal to M, with a view to obtaining an estimation of the symbols of the signals transmitted;

characterized in that each iteration comprises the following steps;

Pre-processing of the vector Y in order to maximize the signal to noise+interference ratio in order to obtain a signal {tilde over (r)}^l,

Subtraction from the signal {tilde over (r)}^l of a signal {circumflex over (z)}^l by means of a subtractor, the signal {circumflex over (x)}^l being obtained by reconstruction post-processing of the interference between symbols from the symbols estimated during the preceding iteration,

Detection of the signal generated by the subtractor in order to obtain, for the iteration in progress, an estimation of the symbols of the signals transmitted;

and in that, the N signals being processed by time intervals T corresponding to the time length of the linear space-time code associated with the transmitted signals, the pre-processing step involves the matrix B in order to maximize the signal to noise+interference ratio, the transfer function of which is;

$B^l=\mathrm{Diag}\left(\frac{1}{{\mathrm{\rho <br><br>}}_{l-1}^2<br><br>A_i^l+\frac{N_0}{E_s}}\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>1\le <br><br>i\le <br><br>\mathrm{MT}·<br><br>C^H<br><br>V^l$$\mathrm{with}<br><br>\text{\hspace{1em}<br><br>}<br><br>V^l={\left[\frac{1-{\mathrm{\rho <br><br>}}_{l-1}^2}{\frac{N_0}{E_s}}·<br><br>C·<br><br>C^H+{\mathrm{Id}}_N\right]}^{-1};<br><br>A^l=\mathrm{diag}<br><br>\left(C^H·<br><br>V^l·<br><br>C\right);<br><br>$

wherein l;

iteration index;

ρ

;

standardized correlation coefficient between the real symbols and the estimated symbols;

N₀;

noise variance;

Es;

mean energy of a symbol;

C;

extended channel matrix;

and in that the post-processing step involves a matrix D for the reconstruction of the interference between symbols, the transfer function of which is;

$D^l=B^l·<br><br>C·<br><br>{\mathrm{\rho <br><br>}}_{l-1}-\mathrm{Diag}\left(\frac{1}{{\mathrm{\rho <br><br>}}_{l-1}^2<br><br>A_i^l+\frac{N_0}{E_s}}\right)<br><br>1\le <br><br>i\le <br><br>\mathrm{MT}$

2. The method according to claim 1, wherein the pre-processing step is carried out by operating a matrix multiplication between the signal vector Y and a matrix B, the matrix B being updated at each iteration.

3. The method according to claim 1, wherein the post-processing step is carried out by operating a matrix multiplication between the vector of the symbols estimated during the preceding iteration and the matrix D, the matrix D being updated at each iteration.

4. The method according to claim 2, wherein for each iteration, the standardized correlation coefficient ρ

is calculated, the updating of a matrix being achieved by determining new coefficients of the matrix as a function of the correlation coefficient obtained for the preceding iteration.

5. The method according to claim 1, wherein in order to determine the correlation coefficient ρ

^l for each iteration;

the signal to interference ratio SINR is calculated using the following formula;

${\mathrm{SINR}}^l=\left[\frac{1}{{\mathrm{\xi <br><br>}}^l<br><br>{\mathrm{e<br><br>}}^{{\mathrm{\xi <br><br>}}^l}<br><br>E_1<br><br>\left({\mathrm{\xi <br><br>}}^l\right)}-1\right]<br><br>\frac{1}{1-{\mathrm{\rho <br><br>}}_{l-1}^2}$

and defining the integral exponential

$E_1<br><br>\left(s\right)={\int <br><br>}_s^{+\mathrm{\infty <br><br>}}<br><br>\frac{e^{-t}}{t}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>t<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{with}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\xi <br><br>}}^l=\frac{\mathrm{<br><br>}}{1-{\mathrm{\rho <br><br>}}_{l-1}^2}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{<br><br>}=\frac{N_0}{{\mathrm{NE}}_s}$

the symbol error probability Pr is calculated from the signal to interference ratio SINR^l; and

the correlation coefficient ρ

^l is then calculated from the symbol error probability Pr.

6. The method according to claim 5, wherein it is assumed that ρ

⁰=0.

7. The method according to claim 5, wherein in order to calculate the symbol error probability Pr it is assumed that the total noise is Gaussian.

8. The method according to claim 7, wherein the formula corresponding to the constellation originating from a linear modulation transmission is used.

9. The method according to claim 5, wherein in order to calculate the correlation coefficient ρ

^l from the symbol error probability Pr, it is assumed that when there is an error, the threshold detector detects one of the closest neighbors to the symbol transmitted.

10. The method according to claim 1, wherein at the final iteration, the signal leaving the subtractor is introduced into a soft-input decoder.

11. The method according to claim 1, wherein the information symbols are elements of a constellation originating from a quadrature amplitude modulation.

12. A space-time decoder implementing a method according to claim 1 for decoding a signal vector Y obtained from N sampled signals in a space-time communication system with M transmission antennae and N receiving antennae, with N greater than or equal to

M, with a view to obtaining an estimation of the symbols of the signals transmitted, characterized in that it comprises:

a pre-processing module of the vector Y for maximizing the signal to noise+interference ratio in order to obtain a signal {tilde over (r)}^l,

a subtractor for subtracting a signal ŝ

^l from the signal {tilde over (r)}^l,

a post-processing module for the reconstruction of the interference between symbols from the symbols estimated during the preceding iteration in order to generate the signal {circumflex over (x)}^l,

a threshold detector for detecting the signal generated by the subtractor in order to obtain, for the iteration in progress, an estimation of the symbols of the signals transmitted;

and in that the N signals being processed by intervals of time T corresponding to the time length of the linear space-time code associated with the transmission signals, the pre-processing module consists of a matrix B for maximizing the signal to noise+interference ratio, the transfer function of which is;

$B^l=\mathrm{Diag}\left(\frac{1}{{\mathrm{\rho <br><br>}}_{l-1}^2<br><br>A_i^l+\frac{N_0}{E_s}}\right)<br><br>1\le <br><br>i\le <br><br>\mathrm{MT}·<br><br>C^H<br><br>V^l$$\mathrm{with}<br><br>\text{\hspace{1em}<br><br>}<br><br>V^l={\left[\frac{1-{\mathrm{\rho <br><br>}}_{l-1}^2}{\frac{N_0}{E_S}}·<br><br>C·<br><br>C^H+{\mathrm{Id}}_N\right]}^{-1};<br><br>A^l=\mathrm{diag}<br><br>\left(C^H·<br><br>V^l·<br><br>C\right);<br><br>$

wherein l;

iteration index;

ρ

;

standardized correlation coefficient between the real symbols and the estimated symbols;

N₀;

noise variance;

Es;

mean energy of a symbol;

C;

extended channel matrix;

and in that the post-processing module consists of a matrix D for the reconstruction of the interference between symbols, the transfer function of which is;

$D^l=B^l·<br><br>C·<br><br>{\mathrm{\rho <br><br>}}_{l-1}-\mathrm{Diag}\left(\frac{1}{{\mathrm{\rho <br><br>}}_{l-1}^2<br><br>A_i^l+\frac{N_0}{E_S}}\right)<br><br>1\le <br><br>i\le <br><br>\mathrm{MT}$

13. The decoder according to claim 12, wherein it comprises a soft input decoder receiving the signal originating from the subtractor during the final iteration.