On the Achievable Rate for Wideband Channels with Estimated CSI

We consider the achievable rate for frequency-selective fading channels when the channel state information (CSI) is to be estimated at the receiver. Since the estimated CSI is not perfect, the achievable rate must be degraded from that with perfect CSI. Using the rate-distortion theory, we study an upper bound on the achievable rate and investigate how the achievable rate can be maximized through an optimization problem by allocating the resources such as degrees of freedom (the transmission time in our work or transmission power) for the exploration of CSI (i.e., the channel estimation) using pilot symbols, and the exploitation of channels to transmit data symbols. Although our study is based on some ideal assumptions, the results could help develop flexible communication systems such as software defined radio (SDR) to achieve a best performance by optimizing radio resources for unknown channels.