Bezout space-time precoders and equalizers for MIMO channels

The transmitter/receiver diversities in p-input-q-output multiple-input multiple-output (MIMO) channels will play a key role in future high-rate wireless communication. The major challenge in MIMO signal recovery is the mitigation of the inevitable intersymbol interference (ISI) and interchannel interference (ICI) in multipath MIMO channels. The Bezout system theory provides a simple solution for ISI/ICI cancellation and, thus, can serve as a powerful mathematical foundation for MIMO systems. If p < q and the MIMO system H(D) is right coprime, the system is perfectly recoverable via a Bezout equalizer. If p > q and the MIMO system H(D) is left coprime, the system is perfectly recoverable via a Bezout precoder, assuming the channel information is available at the transmitter. For a robust channel design, a quantitative analysis of signal-to-noise ratio (SNR) of the optimal Bezout equalizer/precoder can be derived from the Bezout null space. Compared with the Alamouti space-time coding, the Bezout precoder is shown to be more appealing in slowly time-varying channels, where the feedback of the channel information induces minor overhead. The Bezout system can work well jointly with the space-time block coding (STBC). The STBC can be adopted to artificially construct a larger q' x p' (q' > p') virtual transfer function without the channel information. A necessary and sufficient condition is provided for perfect recoverability (PR) for the STBC-induced virtual MIMO systems. Based on the virtual transfer function, both channel-independent and channel-dependent precoding strategies are feasible. Via a singular value decomposition (SVD) analysis, the Bezout precoder can be shown to outperform the orthogonal frequency division multiplexing (OFDM) precoder in bit-error-rate (BER), transmission rate, and receiver implementation. The interplay of the two design parameters (N and rho) is analyzed to provide a simple guideline for an optimal configuration. The combined STBC and Bezout equalization techniques offer a broader spectrum of transceiver system configuration to achieve optimal design tradeoff among BER, transmission rate, and implementation complexity.