Nakagami-m approximations for multiple-input multiple-output singular value decomposition transmissions

The multiple-input multiple-output singular value decomposition (MIMO SVD) modulation is an efficient way of sending data through a multi-antenna communications link in which the transmitter has knowledge of the channel state. Despite its importance, no simple formula for its symbol error rate (SER) has been found, and hence no intuitive characterisation of the quality of this technique for data transmission is available at the present. In this study, the authors present a method for approximating the statistics of each eigenchannel of MIMO SVD using the Nakagami-m fading model. Using the proposed method, it is seen that the SER of the entire MIMO SVD link can be approximated by the average of the SER of Nakagami-m channels. The expression found is simple and yet accurate. This leads to characterise the eigenchannels of N × N MIMO channels with N larger than 14, showing that the smallest eigenchannel distributes as a Rayleigh channel, the next four eigenchannels closely distributes as Nakagami-m channels with m = 4, 9, 25 and 36, and the N - 5 remaining eigenchannels have statistics similar to an additive white Gaussian noise (AWGN) channel within 1 dB signal-to-noise ratio. It is also shown that 75% of the total mean power gain of the MIMO SVD channel goes to the top third of all the eigenchannels.