In this paper, we study the performance of point-to-point communication in spectrum sharing systems under the peak interference power constraint of multiple primary users. In particular, we assume that the channels undergo independent but not necessarily identically distributed Nakagami-m fading with integer values of fading severity parameter m. The cumulative distribution function and probability density function for the signal-to-noise ratio are derived. Based on these formulas, we obtain analytical expressions for the outage probability, the ergodic capacity, and the symbol error probability. Numerical results are also provided to investigate the impact of the peak interference power-to-noise ratio, the number of primary users, and fading parameters on the performance of the secondary network. © 2016 IEEE.