Symbol Error-Rate Analysis of OSTB Codes and Linear Precoder Design for MIMO Correlated Keyhole Channels

Analytical expressions for the symbol error rate (SER) of MIMO systems are important from both design and analysis point of views. This paper derives exact and easy to evaluate analytical expression for the SER of an orthogonal space-time block coded (OSTBC) MIMO system with spatially correlated antennas, in which the channel signal propagation suffers from a degenerative effect known as a keyhole. These expressions are valid for complex valued correlations between antenna elements. Numerical results obtained by simulations are presented to confirm the validity of the analytical SER expressions for several multilevel modulation schemes. Subsequently, a procedure for designing a linear precoder which exploits the knowledge of the channel correlation matrix at the transmitter to enhance the performance of the above system is given. To this end, the exact SER expression is minimized by using a gradient descent algorithm. To demonstrate the performance improvements achievable with the proposed precoder, numerical results obtained in several design examples are presented and compared.