This paper studies a memoryless state-dependent multiple access channel (MAC) where two transmitters wish to convey a message to a receiver under the assumption of causal and imperfect channel state information at transmitters (CSIT) and imperfect channel state information at receiver (CSIR). In order to emphasize the limitation of transmitter cooperation between physically distributed nodes, we focus on the so-called distributed CSIT assumption, i.e. where each transmitter has its individual channel knowledge, while messages can be assumed to be partially or entirely shared a priori between transmitters by exploiting some on-board memory. Under this setup, the first part of the paper characterizes the common message capacity of the channel at hand for arbitrary CSIT and CSIR structure. The optimal scheme builds on Shannon strategies, i.e. optimal codes are constructed by letting the channel inputs be a function of current CSIT only. For a special case when CSIT is a deterministic function of CSIR, the considered scheme also achieves the capacity region of a common message and two private messages. The second part addresses an important instance of the previous general result in a context of a cooperative MIMO Gaussian channel under i.i.d. fading operating in FDD mode, such that CSIT is acquired via an explicit feedback of CSIR. Our optimal scheme applies distributed linear precoding to Gaussian symbols. Surprisingly, we demonstrate that it is suboptimal to send a number of data streams bounded by the minimum between transmit and receive antennas as typically considered in a centralized CSIT setup. Finally, numerical examples are provided to evaluate the sum capacity of the binary MAC with binary states as well as the Gaussian MAC with i.i.d. fading states.
Cooperative multiple-access channels with distributed state information
Submitted to IEEE Transactions of Information Theory, 2021
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