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This paper presents a lower-bound on the ergodic sum capacity of single-input single-output (SISO) opportunistic spectrum sharing multiple access channel (MAC) in Rayleigh fading channels with imperfect channel estimates. Unlike the previous studies, this paper considerers the channel estimation errors for both sets of SISO channels between the secondary user (SU) transmitters and the SU receiver and between the SU transmitters and the primary user receivers. By considering these channel estimation errors, an optimal power allocation policy for each SU transmitter is derived to achieve a lower-bound of the ergodic sum capacity of opportunistic spectrum sharing MAC, subject to a set of SUs transmit power constraints and a set of interference power constraints at each PU receiver. Furthermore, convex optimization techniques are exploited to derive an efficient algorithm to obtain the optimal power allocation for each SU transmitter. Numerical results are presented to illustrate the influences of the channel estimation errors on the ergodic sum capacity.