Expected Likelihood Support for Blind SIMO Channel Identification

SIMO channel identification problems arise in many practical applications, such as geolocation of HF sources propagated via the multi-layer ionosphere. In this case, memory of the channel (often modeled as a finite impulsive response (FIR) channel) makes the traditional assumptions on the channel estimation training samples as independent and identically distributed (i.i.d) invalid. This potentially precludes the use of statistical characteristics typically derived under the i.i.d. assumption, including the Expected Likelihood quality assessment technique. In this paper, we introduce a likelihood-like criteria for this circumstance and demonstrate the practical invariance properties of its distribution for the Expected Likelihood condition, met when the estimated parameters are statistically equivalent to the true ones.