Bilinear Channel Estimation for MIMO OFDM: Lower Bounds and Training Sequence Optimization

Time-varying narrowband Multiple-Input Multiple- Output Orthogonal Frequency Division Multiplexing (MIMO OFDM) channel estimation is considered. The effect of finite bandwidth and practical pulse shapes renders the sparse MIMO-OFDM channel, non-sparse - this effect is denoted leakage. It is shown that the leaked MIMO OFDM channel is effectively separable in the delay and Doppler domains. A convex optimization approach, based on the atomic norm, is posed to estimate the channel parameters. With respect to the mean-squared error, the proposed scheme offers a 4 dB improvement over methods that ignore leakage and a 1.3 dB gain over a method that does consider leakage. The Cramér Rao bound (CRB) for the leaked channel parameters is derived and also exhibits decoupling in delay and Doppler. Training sequences that optimize the CRBs for delay and Doppler parameters are determined via solving key fixed-point equations. The optimized random sequences offer a performance gain on the order of 5-2.5 dB over purely random sequences. The proposed channel estimation algorithm nearly achieves the CRB, suggesting near optimality. Finally, the proposed estimation strategy, when employed on experimental data (SPACE'08), provides an average performance gain of 3 dB with respect to the probability of error in comparison to a traditional sparse channel estimation scheme.