Performance analysis and training power allocation for channel estimation using superimposed training

Channel estimation for single-input multiple-output (SIMO) time-invariant channels using superimposed training has been considered recently by several authors. In particular, J.K. Tugnait and Weilin Luo (see IEEE Commun. Lett., vol.CL-8, p.413-15, 2003) proposed channel estimation using only the first-order statistics of the data under a fixed power allocation for training. We first present a performance analysis of the approach of Tugnait and Luo to obtain a closed-form expression for the channel estimation variance. We then address the issue of superimposed training power allocation for complex Gaussian random (Rayleigh) channels. Using the developed channel estimation variance expression, we cast the power allocation problem as one of optimizing a signal-to-noise ratio (SNR) for equalizer design. Illustrative simulation examples are provided.