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

• US 7,330,519 B2
• Filed: 06/13/2003
• Issued: 02/12/2008
• Est. Priority Date: 06/14/2002
• Status: Expired due to Fees

• Current Assignee: ComSIS Co.
• Original Assignee: ComSIS Co.
• Inventors: Leclair, Philippe
• Primary Examiner(s): Fan; Chieh M.
• Assistant Examiner(s): Perilla; Jason M.
• Application Number:
  US10/517,026
• Publication Number:
  US 20060050804A1
• Time in Patent Office: 1,705 Days
• Field of Search: 375/316, 375/295, 375/340, 375/346
• US Class Current: 375/316
• 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^1−l) 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 and M being integers and N greater than or equal to M, with a view to obtaining an estimation of symbols of signals transmitted;

characterized in that each iteration comprises the following steps;

Pre-processing of the vector Y in order to maximize a 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 (z)}^l being obtained by reconstruction post-processing of an interference between symbols of an iteration in progress from symbols estimated during a preceding iteration,

Detection of a 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 a time length of a linear space-time code associated with the signals transmitted, the pre-processing step utilizes a matrix B in order to maximize the signal to noise+interference ratio, a transfer function of which is;

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

wherein Λ

;

iteration index;

ρ

;

standardized correlation coefficient between real symbols and estimated symbols;

N₀;

noise variance;

Es;

mean energy of a symbol;

C;

extended channel matrix;

Id_N;

identity matrix of size N;

C^H;

conjugate transpose of C;

i;

index ranging from 1 to MT;

and in that a post-processing step involves a matrix D for the reconstruction of the interference between symbols, a 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 estimation of the symbols of the signals transmitted 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 and the matrix B is updated, the updating of the matrix B being achieved by determining new coefficients of the matrix B as a function of the correlation coefficient obtained for a 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 noise+interference ratio SINR for each iteration 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

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

with ξ

^l=ζ

/1−

ρ

<sub>l−

1</sub>² and ζ

=N₀/NE_S

a symbol error probability Pr is calculated from the signal to noise+interference ratio SlNR^l for each iteration; and

the correlation coefficient ρ

^l for each iteration is then calculated from the respective symbol error probability Pr for the given iteration.

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, in obtaining an estimation of the symbols of the signals transmitted, a formula corresponding to a constellation originating from a linear modulation transmission technique is used.

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

^l for each iteration using its respective symbol error probability Pr, it is assumed that when there is an error, a threshold detector detects one of among closest neighbors to a symbol transmitted.

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

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

12. A space-time decoder 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 and M being integers and N greater than or equal to M, with a view to obtaining an estimation of symbols of signals transmitted, characterized in that it comprises:

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

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

a subtractor for subtracting a signal {circumflex over (z)}^l from the signal {tilde over (r)}^l,

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

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

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

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;

Id_N;

identity matrix of size N;

C^H;

conjugate transpose of C;

i;

index ranging from 1 to MT;

and in that the post-processing module consists of a matrix D for the reconstruction of the interference between symbols, a 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 further comprises a soft input decoder receiving the signal generated from the subtractor during a final iteration.