Reduced-complexity multiple-input multiple-output (MIMO) channel detection via sequential Monte Carlo
A detection system and method are disclosed which uses sequential Monte Carlo techniques in a multiple-input multiple-output system. The detection system and method samples a first and second component of the modulation symbols separately, thereby reducing the number of symbol candidates and the computational complexity of the system.
1. A method for demodulating data from a channel, comprising:
receiving a priori probability values for symbols transmitted across the channel, each symbol decomposable into a first symbol component and a second symbol component;
in accordance with the a priori probability values, determining a first set of Monte Carlo samples of the first symbol components weighted with respect to a probability distribution of the first symbol components and determining a second set of Monte Carlo samples of the second symbol components, where the first symbol components and the second symbol components are sampled independently;
estimating a posteriori probability values for the symbols based on the first and second sets of Monte Carlo samples, and
wherein the weighted sets of Monte Carlo samples are determined by:
sequentially iterating on a spatial domain of transmit antennas where the probability distribution of the first symbol components and the second symbol components is with respect to received signals after a coordinate rotation obtained by QR decomposition
enumerating first and second symbol component samples for a first portion of the spatial domain of the transmit antennas in accordance with a deterministic computation of the probability distributions of the first and second symbol components;
updating importance weights for the first symbol components using the enumerated first symbol component samples, preserving only a subset of sequences of first symbol components based on the importance weights for the first symbol components;
updating importance weights for the second symbol components using the enumerated second symbol component samples, preserving only a subset of sequences of second symbol components based on the importance weights for the second symbol components;
wherein the updating steps are performed while sequentially iterating on a second portion of the spatial domain of the transmit antennas.
2. The method of claim 1 wherein the step of determining the weighted sets of Monte Carlo samples further comprises:
drawing the first set of Monte Carlo samples from a trial distribution specified for the first symbol components;
updating importance weights for the first set of Monte Carlo samples based on deviations of the trial distribution specified for the first symbol components from the probability distribution of the first symbol components;
drawing the second set of Monte Carlo samples from a trial distribution specified for the second symbol components; and updating importance weights for the second set of Monte Carlo samples based on deviations of the trial distribution specified for the second symbol components from the probability distribution of the second symbol components;
wherein the above steps are performed while sequentially iterating on a spatial domain of the transmit antennas.
3. The method of claim 2 , wherein m is a number of Monte Carlo samples determined for a symbol interval and the weighted Monte Carlo samples for the first symbol components are represented by {(s r,k (j) , w r,k (j) )}, and the weighted Monte Carlo samples for the second symbol components are represented {(s i,k (j) , w i,k (j) )}, where the a posteriori probability value for the first symbol component is estimated by:
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and where the a posteriori probability value for the second symbol component is estimated by:
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where j is a sample index, k is an index identifying a transmit antenna, z is a vector of received signals from different transmit antennas after nulling, A is an alphabet set from which symbols take their the values, a i is an ith value in A, W k Σ j=1 m w k (j) ; and Π(·) is an indicator function.
4. The method of claim 1 ,wherein m is a number of Monte Carlo Samples determined for a symbol interval and the weighted Monte Carlo samples for the first symbol components are represented by {(s i,k (j) , w i,k (j) )}, and the weighted Monte Carlo samples for the second symbol components are represented by {(s r,k (j) , w r,k (j) )}, and where the a posteriori probability value for the first symbol component is estimated by:
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and where the a posteriori probability value for the second symbol component is estimated by:
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where j is a sample index, k is an index identifying a transmit antenna, z is a vector of received signals from different transmit antennas after nulling, A is an alphabet set from which symbols take their values, a i is an ith value in A, W k Σ j=1 m w k (j) ; and Π(·) is an indicator function.
5. The method of claim 1 , wherein the first symbol component of each symbol is a real component of the symbol and wherein the second symbol component of each symbol is an imaginary component of the symbol.
6. The method of claim 1 , wherein the channel is a multiple-input multiple-output system.