**7. Conclusions**

276 Wireless Communications and Networks – Recent Advances

Fig. 7. Lower bound of the average channel capacity versus different values of ST power

received SNR for different frame length. It is observed that the increment of SNR leading to a corresponding increase in the optimal ST power allocation factor. This can be easily comprehended that according to (41), the effective interference is composed of two factors, i.e. the bias of channel estimation and the additive noise. That is, for large SNRs, higher

required to improve the channel estimation performance, thus leading to a reduction of the effective interference. Conversely, when SNR is small, improving the channel estimation accuracy has a small effect in reducing the effective interference. On the other hand, we

have theoretically analyzed in Section III that the estimation variance approaches to a fixed lower bound that can be only improved by increasing ST power allocation when the frame length is large enough. Therefore, the power allocated to the training sequence can be reduced with no loss in channel estimation performance when the frame length is increased, but finally approaches to a fixed lower bound associate with the channel estimation variance

when is sufficiently large. This is somewhat different from those presented in [10].

decreases as the frame length increases but approximately unvaried when is

is almost unchanged when 192 *I* . This result arises because we

versus

> is

under SNR = 0dB, 10dB and 20dB, respectively.

Fig. 8 shows the plots of the optimal value of training power allocation factor

allocation factor

notice that

sufficiently large, i.e.

In this paper, we have a developed superimposed training-aided LTV channel estimation approach for MIMO/OFDM systems. The LTV channel coefficients were firstly modeled by truncated DFB, and then estimated by using a two-step approach over multiple OFDM symbols. We also present a performance analysis of the proposed estimation approach and derive closed-form expressions for the channel estimation variances. It is shown that the estimation variances, unlike the conventional ST, approach to a fixed lower-bound that can only be reduced by increasing the pilot power. Using the developed channel estimation variance expression, we analyzed the system capacity and optimize the training power allocation by maximizing the lower bound of the average channel capacity for systems with a limited power. Compared with the existing FDM training based schemes, the new estimator does not entail a loss of rate while yields a better estimation performance, and thus enables a higher efficiency.
