Lattice Coding and Decoding for Multiple-Antenna Ergodic Fading Channels

For ergodic fading, a lattice coding and decoding strategy is proposed and its performance is analyzed for the single-input single-output (SISO) and multiple-input multiple-output (MIMO) point-to-point channel as well as the multiple-access channel (MAC), with channel state information available only at the receiver (CSIR). At the decoder a novel strategy is proposed consisting of a time-varying equalization matrix followed by decision regions that depend only on channel statistics, not individual realizations. Our encoder has a similar structure to that of Erez and Zamir. For the SISO channel, the gap to capacity is bounded by a constant under a wide range of fading distributions. For the MIMO channel under Rayleigh fading, the rate achieved is within a gap to capacity that does not depend on the signal-to-noise ratio (SNR), and diminishes with the number of receive antennas. The analysis is extended to the $K$ -user MAC where similar results hold. Achieving a small gap to capacity while limiting the use of CSIR to the equalizer highlights the scope for efficient decoder implementations, since decision regions are fixed, i.e., independent of channel realizations.

对于千古褪色，提出了晶格编码和解码策略，并分析了单输入单输出（SISO）和多输入多输出（MIMO）的性能，以及多个点对点通道访问通道（MAC），仅在接收方（CSIR）上获得频道状态信息。在解码器上，提出了一种新的策略，该策略由随时间变化的均衡矩阵组成，然后是仅取决于信道统计的决策区域，而不是个人实现。我们的编码器具有与Erez和Zamir相似的结构。对于SISO通道，在各种褪色的分布下，容量的差距是由常数界定的。对于瑞利褪色下的MIMO通道，所达到的速率在于不取决于信噪比（SNR）（SNR）的容量差距范围内，并且随接收天线的数量减少。分析扩展到$ k $ - 用户Mac，在该Mac中得出了类似的结果。在限制CSIR向均衡器的情况下实现较小的差距，突出了有效解码器实现的范围，因为决策区是固定的，即独立于渠道实现。