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Estimating the number of signals embedded in noise is a fundamental problemin signal processing. As a classic estimator based on random matrix theory(RMT), the RMT estimator estimates the number of signals via sequentiallytesting the likelihood of an eigenvalue as arising from a signal or noise for agiven over-detection probability. However, it tends to under-estimate thenumber of signals as weak signal eigenvalues may be immersed in thenon-negligible bias term among eigenvalues for finite sample size. In order tosolve this problem, we propose an RMT estimator with adaptive decisioncriterion (termed as RMT-ADC estimator) by adaptively incorporating the biasterm into the decision criterion of the RMT estimator. Firstly, we analyze theeffect of this bias term among eigenvalues on the estimation performance of theRMT estimator. Then, we derive both the decreased over-estimation probabilityand the increased under-estimation probability of the RMT estimator incurred bythe bias term when assuming the eigenvalue being tested is arising from asignal, and also derive the increased under-estimation probability of the RMTestimator incurred by the bias term when assuming the eigenvalue being testedis arising from noise. Based on these results, the RMT-ADC estimator canadaptively determine whether the noise variance should be estimated under theassumption that the eigenvalue being tested is arising from a signal or fromnoise, and thus can adaptively select its decision criterion. Moreover, theRMT-ADC estimator can adaptively determine whether the bias term amongeigenvalues should be incorporated into the selected decision criterion or not.Therefore, the RMT-ADC estimator can avoid the higher under-estimationprobability of the RMT estimator. Finally, simulation results are presented toshow that the proposed RMT-ADC estimator significantly outperforms the existingestimators.

RMT Estimator with Adaptive Decision Criteria for Estimating the Number of Signals Based on Random Matrix Theory