Near-optimal multiple-input multiple-output (MIMO) channel detection via sequential Monte Carlo

• US 7,317,770 B2
• Filed: 07/31/2003
• Issued: 01/08/2008
• Est. Priority Date: 02/28/2003
• Status: Expired due to Fees

• Current Assignee: NEC Corporation
• Original Assignee: NEC Laboratories America Inc (NEC Corporation)
• Inventors: Wang, Xiaodong
• Primary Examiner(s): WANG, TED M
• Application Number:
  US10/631,991
• Publication Number:
  US 20040174939A1
• Time in Patent Office: 1,622 Days
• Field of Search: 375/340, 375/347, 375/324, 375/267, 375/260
• US Class Current: 375/340
• CPC Class Codes: H04L 1/005 Iterative decoding, including iteration between signal detection and decoding operation
• CPC Class Codes: H04L 1/0055 MAP-decoding
• CPC Class Codes: H04L 1/0618 Space-time coding

Abstract

A class of soft-input soft-output demodulation schemes for multiple-input multiple-output (MIMO) channels, based on the sequential Monte Carlo (SMC) framework under both stochastic and deterministic settings. The stochastic SMC sampler generates MIMO symbol samples based on importance sampling and resampling techniques, while the deterministic SMC approach recursively performs exploration and selection steps in a greedy manner. By exploiting the artificial sequential structure of the existing simple Bell Labs Layered Space Time (BLAST) detection method based on nulling and cancellation, the proposed algorithms achieve an error probability performance that is orders of magnitude better than the traditional BLAST detection schemes while maintaining a low computational complexity. Performance is comparable with that of the sphere decoding algorithm, with a much lower complexity. Both the stochastic and deterministic SMC detectors can be employed as the first-stage demodulator in an iterative or turbo receiver in coded MIMO systems.

Claims

1. A method for demodulating data from a multiple-input multiple-output (MIMO) channel, comprising:

receiving a priori probability values for symbols transmitted across the MTNO channel, said a priori probability values are represented by P(s_k=a_i), where the symbols in a symbol interval are represented by s_k, and k is an index identifying a transmit antenna; and

a_i is an ith value in an alphabet set from which the symbols take their values;

in accordance with the a priori probability values, determining a set of Monte Carlo samples of the symbols weighted with respect to a probability distribution of the symbols; and

estimating a posteriori probability values for the symbols based on the set of Monte Carlo samples.

2. The method of claim 1, wherein:

the Monte Carlo samples comprise stochastic Monte Carlo samples.

3. The method of claim 1, wherein:

the probability distribution of the symbols is represented by p(s|z), where s is a vector of transmitted signal values for different transmit antennas in a symbol interval, and z is a vector of received signals from the different transmit antennas after nulling.

4. The method of claim 1, wherein determining the set of Monte Carlo samples of the symbols in a symbol interval, represented by {(s_k^(j), w_k^(j))}, comprises:

determining a trial sampling density for each ith value, a_i, in an alphabet set A from which the symbols take their values, using the a priori probability value P(s_k=a_i) from a previous iteration, where the symbols are represented by s_k, and k is an index identifying a transmit antenna;

drawing the jth sample symbol s_k^(j), from the alphabet set A, where j=1,2, . . . ,m, and m is a number of the Monte Carlo samples determined for the symbol interval; and

computing an importance weight w_k^(j) for s_k^(j).

5. The method of claim 4, further comprising:

performing resampling to obtain updated importance weights w_k^(j).

6. The method of claim 4, further comprising:

initializing the importance weights w<sub>−

1</sub>^(j)=1.

7. The method of claim 1, wherein:

m is a number of the Monte Carlo samples determined for a symbol interval;

the Monte Carlo samples are represented by {(s_k^(j)), w_k^(j))},

each a posteriori probability value P(s_k=a_i|z) is obtained from

$P<br><br>\left(s_k=a_i|z\right)=\frac{1}{W_k}<br><br>\underset{j=1}{\overset{m}{\sum <br><br>}}<br><br><br><br>1<br><br>\left(s_k^{\left(j\right)}=a_i\right)<br><br>w_k^{\left(j\right)},a_i\in <br><br>A$

where

z is a vector of received signals from different transmit antennas after nulling;

the symbols are represented by S_k, where k is an index identifying a transmit antenna;

importance weights for the symbols S_k are represented by w_k;

A is an alphabet set from which the symbols take their values, and a_u is an ith value in A;

$W_k<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\underset{j=1}{\stackrel{m}{\sum <br><br>}}<br><br>w_k^{\left(j\right)};<br><br>$

and

1 is an indicator function defined by

$1<br><br>\left(x=a\right)=\{\begin{array}{c}1,\mathrm{if}<br><br><br><br>x=a,\\ 0,\mathrm{if}<br><br><br><br>x\ne <br><br>a.\end{array}$

8. The method of claim 1, further comprising:

based on the a posteriori probability values, calculating a posteriori log-likelihood ratios of interleaved code bits.

9. The method of claim 1, wherein:

the Monte Carlo samples comprise deterministic Monte Carlo samples.

10. The method of claim 1, wherein determining the set of Monte Carlo samples of the symbols in a symbol interval, represented by {(s_k^(j), w_k^(j))}, comprises:

calculating an exact expression for the probability distribution by enumerating m samples for less than all transmit antennas to obtain m data sequences, where m is a number of the Monte Carlo samples determined for the symbol interval;

computing the importance weight w_k^(j) for each symbol s_k^(j), where k is an index identifying a transmit antenna; and

selecting and preserving m distinct data sequences with the highest weights.

11. A program storage device tangibly embodying a program of instructions executable by a machine to perform a method for demodulating data from a multiple-input multiple-output (MIMO) channel, the method comprising:

receiving a priori probability values for symbols transmitted across the MIMO channel, said a priori probability values being represented by P(s_k=a_i), where the symbols in a symbol interval are represented by s_k, and k is an index identifying a transmit antenna; and

a_i is an ith value in an alphabet set from which the symbols take their values;

in accordance with the a priori probability values, determining a set of Monte Carlo samples of the symbols weighted with respect to a probability distribution of the symbols; and

estimating a posteriori probability values for the symbols based on the set of Monte Carlo samples.

12. A demodulator for demodulating data from a multiple-input multiple-output (MIMO) channel, comprising:

means for receiving a priori probability values for symbols transmitted across the MIMO channel, said a PRIORI probability values being represented by P(s_k=a_i), where the symbols in a symbol interval are represented by s_k, and k is an index identifying a transmit antenna; and

a_i is an ith value in an alphabet set from which the symbols take their values;

means for determining, in accordance with the a priori probability values, a set of Monte Carlo samples of the symbols weighted with respect to a probability distribution of the symbols; and

means for estimating a posteriori probability values for the symbols based on the set of Monte Carlo samples.

13. The demodulator of claim 12, wherein:

the Monte Carlo samples comprise stochastic Monte Carlo samples.

14. The demodulator of claim 12, wherein:

the Monte Carlo samples comprise deterministic Monte Carlo samples.

15. A method for demodulating data from a channel, the channel comprising a multiple-input multiple-output (MIMO) channel, the method comprising:

(a) receiving a priori probability values for symbols transmitted across the channel;

(b) in accordance with the a priori probability values, determining a set of deterministic Monte Carlo samples of the symbols in a symbol interval, represented by {s_k^{(j), w}_k^(j))}, weighted with respect to a probability distribution of the symbols, by;

(b1) calculating an exact expression for the probability distribution by enumerating m samples for less than all transmit antennas to obtain m data sequences, where m is a number of the deterministic Monte Carlo samples determined for the symbol interval;

(b2) computing the importance weight w_k^(j) for each symbol s_k^(j), where k is an index identifying a transmit antenna; and

(b3) selecting and preserving m distinct data sequences with the highest weights; and

(c) estimating a posteriori probability values for the symbols based on the set of deterministic Monte Carlo samples;

wherein;

(d) the probability distribution of the symbols is represented by p(s|z), where s is a vector of transmitted signal values for different transmit antennas in a symbol interval, and z is a vector of received signals from the different transmit antennas after nulling.

16. A method for demodulating data from a channel, the channel comprising a multiple-input multiple-output (MIMO) channel, the method comprising:

(a) receiving a priori probability values for symbols transmitted across the channel;

(b) in accordance with the a priori probability values, determining a set of deterministic Monte Carlo samples of the symbols in a symbol interval, represented by {(s_k^(j), w_k^(j))}, weighted with respect to a probability distribution of the symbols, by;

(b1) calculating an exact expression for the probability distribution by enumerating m samples for less than all transmit antennas to obtain m data sequences, where m is a number of the deterministic Monte Carlo samples determined for the symbol interval;

(b2) computing the importance weight w_k^(j) for each symbol s_k^(j), where k is an index identifying a transmit antenna; and

(b3) selecting and preserving m distinct data sequences with the highest weights;

(c) estimating a posteriori probability values for the symbols based on the set of deterministic Monte Carlo samples;

wherein;

(d) wherein the probability distribution of the symbols is represented by p(s|z), where s is a vector of transmitted signal values for different transmit antennas in a symbol interval, and z is a vector of received signals from the different transmit antennas after nulling;

(e) wherein m is a number of the deterministic Monte Carlo samples determined for a symbol interval;

each a posteriori probability value P(s_k=a_i|z) is obtained from

$P<br><br>\left(s_k=a_i|z\right)=\frac{1}{W_k}<br><br>\underset{j=1}{\stackrel{m}{\sum <br><br>}}<br><br>1<br><br>\left(s_k^{\left(j\right)}=a_i\right)<br><br>w_k^{\left(j\right)},a_i\in <br><br>A$

where

z is a vector of received signals from different transmit antennas after nulling;

A is an alphabet set from which the symbols take their values, and a_i is an ith value in A;

$W_k<br><br>\stackrel{\mathrm{\Delta <br><br>}}{=}<br><br>\underset{j=1}{\stackrel{m}{\sum <br><br>}}<br><br>w_k^{\left(j\right)};<br><br>$

and

1 is an indicator function defined by

$1<br><br>\left(x=a\right)=\{\begin{array}{c}1,\mathrm{if}<br><br><br><br>x=a,\\ 0,\mathrm{if}<br><br><br><br>x\ne <br><br>a,\end{array}$

and

(f) calculating, based on the a posteriori probability values, aposteriori log-likelihood ratios of interleaved code bits.