An Analytical Approach to Optimal Signal Design for Wireless Communication Channels

In this paper, we formulate an optimal signal design for time varying wireless communication channels. Wireless channels in a practical scenario suffer from impairments like fading due to multipath effects and time varying characteristics resulting in varying signal strength at the receiver. Decoding of the signal becomes unreliable when the received signal strength is lower than the noise power. To tackle this issue, we here take a control theory based approach to design optimal signal such that signal strength at the receiver is maximized. In this approach, the wireless channel is considered to be a linear system where the input to the system is the transmitted signal and output is the received signal at the receiver. We here analyze the influence of fading on the transmitted signal and formulate an optimal signal design for single input and single output (SISO) operation and multiple input and multiple output (MIMO) operation. We analytically prove that the optimal signal constitutes a stable state of a continuous time Hopfield neural network.