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We consider an added level of adaptation to classical weighted least-squares (WLS) by adapting the forgetting factor α using a stochastic approximation (SA) algorithm, thus obtaining the modified WLS algorithm. The SA adapts α to the random operating conditions and leads to improved performance over the case where α is fixed. Modified WLS has wide applicability in systems operating in random environments which are difficult to predict. We focus on a wireless adaptive antenna array application where one wishes to detect the signal from a desired user (i.e. "reference signal") where the operating conditions are changing due to the mobility and channel variations. In a work by Buche and Kushner, (2003), the SA for adapting α was analyzed and the modified WLS algorithm was investigated in simulations of the line-of-sight (LOS) channel case where the reference signal is known. Here we extend the simulation study to cases where the channel is Ricean and Rayleigh and also consider the case where the known reference signal is replaced by a periodically blind signal. The great benefit of the modified WLS is demonstrated. The periodically blind signaling case leads to new issues in the stochastic approximation analysis which we discuss.