Cramer-Rao lower bound for semiblind channel estimation with respect to coded and uncoded finite-alphabet signals

Within this paper we derive the Cramer-Rao lower bound (CRLB) for semiblind channel estimation with respect to coded or uncoded finite alphabet source signals in finite impulse response systems. Since the obtained solution incorporates a high dimensional integral, which can only be solved numerically, we approximate the CRLB for low and high signal to noise ratio (SNR). We also examine the SNR range where the CRLB crosses over from the low to the high SNR approximation. It is shown that the crossover range depends on the modulation index and code characteristics. Combining the approximations for high and low SNR and estimating the crossover range yields an overall approximation, which can easily be calculated also for more complex scenarios. It is shown that the approximation meets the true CRLB very well.