Approximate full diversity equalizers for doubly selective channels

It is known that linear minimum mean square error zeroforcing (MMSE-ZF) equalization can achieve full joint multipath-Doppler diversity offered by doubly selective channels [1] when appropriate precoding is applied at the transmitter. However, brute force implementation MMSEZF equalizer involves a matrix inversion operation that results in significant computational burden. In order to alleviate this problem, first an iterative implementation ofMMSEZF equalizer based on polynomial expansion (PE) approximation is proposed. Then, the structure of a matrix involved in this approximation is exploited to reduce the computational complexity of the PE approximation. Simulation results are provided to show that while this approach reduces the computational complexity compared to the brute-force  implementation of the MMSE-ZF equalizer, it does not effect the diversity order.