Exact bit error probabilities and packet error statistics for SVD transmission over time-varying dual-branch MIMO systems obtained by a Markov model

Using a finite state Markov channel model, we develop an analytical method for evaluation of the packet error structure in multiple-input multiple-output (MIMO) systems based on singular value decomposition (SVD). We consider dual-branch MIMO systems, with either two transmit and arbitrary number of receive antennas, or arbitrary number of transmit and two receive antennas. The corresponding Markov model parameters are obtained using a novel closed-form expressions for probability density function and level crossing rate of the signal-to-noise ratio at the output of eigenchannels in a MIMO system, derived for a case of Rayleigh propagation, imperfect channel state information and any fixed power allocation. The exact bit error rate for the transmission of quadrature amplitude modulated (QAM) symbols through the eigenchannels is derived in polynomial closed form. Furthermore, by using the developed Markov model, the packet error statistics in the corresponding eigenchannels are determined, and the closed-form analytical expression for the system throughput is derived when ‘go-back-N’ automatic repeat request procedure is applied in time-varying eigenchannels. The analytical results are validated by using Monte Carlo simulations.