Analysis and Optimization of Diagonally Layered Lattice Codes for MIMO Rayleigh Fading Channels

A class of space-time block codes is proposed and optimized for the quasi-static multi-input multi-output (MIMO) Rayleigh fading channel. These codes use single-input single-output (SISO) component codes based on algebraic number theory in a diagonally layered architecture, and are hence referred to as diagonally layered lattice (DLL) codes. A salient feature of the DLL codes is that they have nearly full rate and a lower decoding complexity than other existing full rate codes, and yet they guarantee a high diversity order. The idea of code design advocated here differs from that of the prevalent code design methods which sacrifice rate for reduction in decoding complexity in that it makes a more judicious trade-off between rate, performance and complexity. Based on a pairwise error probability analysis, it is shown that the diversity order of the frame error probability (FEP) of the proposed codes decoded via the zero forcing filter isNK K(K 1)=2 in aN receive andK transmit antenna system with N K. The error probability analysis also yields design criteria which are then used to find optimal transmit power allocations and good SISO component codes. A novel soft decision feedback decoder is proposed to mitigate error propagation. It is shown that in spite of the much lower decoding complexity, the FEP performance of the DLL codes for moderate-to-high spectral efficiencies and a wide range of SNRs is generally close to the performance offered by the best performing space-time block codes (STBCs) known to date. Furthermore, for MIMO systems with a low decoding complexity constraint, it is shown that the DLL codes proposed in this paper significantly outperform existing STBCs.