Throughput optimization for cognitive radios under sensing uncertainty

The efficiency of a cognitive radio system depends critically on sensing reliability since post-sensing communication efficiency is subject to optimal resource allocation under this sensing uncertainty. In this paper, we develop online algorithms for maximizing throughput in a cognitive radio when the sensing outcome of the primary channel (available/unavailable) is not always reliable. We first develop a very efficient per-slot power allocation algorithm for a secondary user transmitting under total power constraints over a period of M time slots, assuming reliable sensing during each slot but with no look-ahead capability. Specifically, we show that it is always possible to achieve a transmission rate that is a constant fraction of the optimal transmission rate even with no apriori knowledge of the number of available slots. Our online power-allocation algorithm is 3.7-competitive, i.e the rate achieved by this algorithm is within a factor of 2.5/ln 2 <; 3.7 of the optimal rate that can be achieved by a genie-aided algorithm with full look-ahead knowledge of channel availability during the M slots. Then we analyze the impact of sensing errors on algorithm performance. We show that the online algorithm is still constant-factor competitive with very high probability (≥ 1 - 1/M) even with sensing errors under the worst-possible input sequence, provided the number of good time slots is reasonably large as a function of M. However, when the number of good time slots is small (M⁰⁽¹⁾, for example √(M)), we show that no online algorithm can achieve a constant-factor competitive ratio.