Distribution of Inner Product of Two Complex Gaussian Vectors and its Application to MPSK Performance

Consider two independent complex Gaussian vectors having arbitrary mean vectors and covariance matrices which are scaled versions of the identity matrix. The joint characteristic function (c.f.) of the real and imaginary parts of the inner product of these two vectors is derived in closed form. This joint c.f. is applied to the analysis of the symbol error probability (ESP) of a multibranch diversity reception system in flat Rayleigh fading using M-ary phase-shift keying (MPSK). The receiver employs maximal- ratio combining with least squares channel estimation by means of pilot symbols. Closed form expressions of the SEP are obtained for the cases of binary phase-shift keying, MPSK with high signal- to-noise ratio approximation, and MPSK with independent and identically distributed fading.