Analysis and Optimization of Diagonally Layered Lattice Schemes for MIMO Fading Channels

Embodiments of the diagonal Bell Laboratories layered space-time (D-BLAST) architecture for multiple-input-multiple-output (MIMO) communication are developed wherein information symbol vectors are encoded using codewords from a lattice code [called a diagonally layered lattice (DLL) code], which are formatted onto the diagonals of a space-time frame. Decoding is done using a sphere decoder for each diagonal based on soft statistics obtained after zero forcing (ZF) or minimum-mean-square-error (MMSE) filtering and decision feedback. These operations give rise to an effective parallel channel model with channel gains with nonidentical statistics and additive noise which is Gaussian in the ZF-filtering case and non-Gaussian in the MMSE-filtering case. The so-called full modulation diversity (FMD) property is nevertheless shown to yield the maximum achievable diversity orders over the MIMO channel for both the ZF- and the MMSE-filtering-based decoders respectively, for any arbitrary fading distribution. In the case of the independent, identically distributed (i.i.d.) Rayleigh fading MIMO channel with
K
-transmit and
N
-receive antennas (with
N
ges
K
), these diversity orders are
NK
-
K
(
K
-1)/2 and
NK
for ZF- and MMSE-filtering-based decoding, respectively. The error probability analysis also yields a design criterion for optimizing transmit power allocations. Several lattice design methods are proposed for the effective parallel channel models. Two methods are proposed to achieve high coding gain in the Rayleigh fading MIMO channel; a third method is proposed that minimizes the exact symbol error probability (SEP) and can be tailored for any given fading distribution. A novel soft decision feedback decoder is also proposed based on the list sphere decoder to mitigate error propagation due to hard decision feedback. The salient feature of the proposed DLL schemes is that they have nearly full rate and full (or high) diversity order and yet a much lower decoding complexity than other existing full rate, full diversity space-time block codes (STBCs). The frame error probability (FEP) performance of the optimized DLL schemes for moderate-to-high spectral efficiencies and a wide range of signal-to-noise ratios (SNRs) can be quite close to the performance of the best performing, but more complex to decode, STBCs. Moreover, the proposed DLL schemes significantly outperform other existing MIMO systems of comparable decoding complexity.