Decoding for MIMO systems with imperfect channel state information

We consider robust receiver design in uncoded multiple-input multiple-output (MIMO) wireless communication systems. In practical systems, the channel state information (CSI) available at the receiver is often imperfect due to measurement errors, quantization errors and many other sources of errors. Consequently, using the erroneous CSI for decoding the transmitted symbols will significantly degrade the symbol error rate (SER) performance of any decoding schemes. In this paper, we formulate and implement a decoder for MIMO systems with imperfect CSI. The proposed decoder is the maximum likelihood (ML) decoder under imperfect receiver CSI, which is the optimal decoder. This "robust" decoder has exponential complexity; with the goal of reducing its complexity, we propose a recursive search algorithm which is akin to a modified form of sphere decoding. We verify, via numerical simulation, that the recursive search algorithm (termed as robust sphere decoder) achieves performance almost the same as the ML solution, with significantly lower computational complexity. For a 2 x 2 256QAM system, the robust sphere decoder compares approximately 4500 solutions in contrast to 65536 comparisons using a brute-force search method. In addition, the proposed decoder has a significant performance improvement over conventional ML decoding that ignores channel estimation error. For a 2 x 2 16QAM system, where the variance of the CSI error ranges ranges from 0.1 to 10 times the variance of the additive noise, and at SER of 10^-3, the proposed decoder has a 4.5dB gain over the conventional ML decoder.