Non-coherent space-time trellis-coded modulations for network-coded wireless relay communications

A method for jointly optimizing signal constellations, channel coding and network coding in a network including a first terminal transceiver, a second terminal transceiver and a relay transceiver, comprising the steps of:

• initializing, which comprises the steps of:
• generating a first codebook [Xa] for the first transceiver and a second codebook [Xb] for the second transceiver;
• constructing a compound codebook [Xab] from the first codebook [Xa] and the second codebook [Xb];
• and
• initializing a network coding function;
• optimizing of a trellis-coded modulation (TCM), which comprises the steps of:
• determining a distance of a compound TCM for all possible pairs of codewords Xab in the compound codebook [Xab] along a trellis-state diagram;
• excluding the pairs of codewords that have an identical network coding output;
• selecting the pairs of codewords Xab having minimum distances as dominant codeword pairs;
• and
• updating the pairs of dominant codewords by a gradient procedure over a Grassmannian manifold, and iterating over the optimization of the TCM until convergence to produce a network coding function to jointly optimize the signal constellations and the channel coding;
• and
• optimizing the network coding function, which comprises the steps of:
• maximizing the pairs of dominant codewords, and iterating over the optimizing of the TCM and the optimizing of the network coding function until the network coding function is identical over two successive iterations to jointly optimize the signal constellations, the channel coding and the network coding, wherein the steps are performed in processors.