On superimposed training for channel estimation: Performance analysis, training power allocation, and frame synchronization

Channel estimation for single-input multiple-output (SIMO) time-invariant channels using superimposed training has been recently considered by several authors. A periodic (non-random) training sequence is arithmetically added (superimposed) at a low power to the information sequence at the transmitter before modulation and transmission. In particular, in [10], the channel is estimated using only the first-order statistics of the data under a fixed power allocation to training and under the assumption that the superimposed training sequence at the receiver is time-synchronized with its transmitted counterpart (frame synchronization). In this paper, we remove these restrictions. We first present a performance analysis of the approach of [10] 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 for equalizer design. Finally, we propose a novel approach for frame synchronization. All the results are illustrated via simulation examples involving frequency-selective Rayleigh fading. Simulation comparisons with an existing approach to frame synchronization is also provided.