Distance spectrum computation for equalized MIMO multipath fading channels

We estimate bit error probability bounds for finite-length delay-optimised multi-input multi-output (MIMO) equalizers. These equalizers shorten the impulse response memory of frequency-selective MIMO channels by minimizing the average energy of the error sequence between the equalized MIMO channel impulse response and the target impulse response. We answer an important question in this paper namely, how much asymptotic loss in SNR do we expect as a result of this shortening? A partial distance spectrum for a 2×2 MIMO channel is evaluated with or without channel shortening equalisers. The union bound is then used to upper bound the bit error probability. Similarly, the lower bound is computed from the squared minimum Euclidean distance. Numerical results show that the expected loss is in the order of 2.5 dB for realistic wireless channel environments