PSK constellations for good diversity on fading channels

For the case of simultaneous phase shift keyed (PSK) transmission over multiple channels when each channel has independent fading, a new constellation on the space formed by the different channels is described. The constellation has good performance when there is no fading and provides diversity for good performance during fades. It is bandwidth efficient, requires no interleaving or delay, and is relatively simple. The maximum likelihood receiver for the constellation is presented; it forms instantaneous memoryless decisions. The error probability is derived in the presence of independent Rayleigh fading. Examples of the new constellation are shown to gain 2 to 4 dB in signal-to-noise ratio over symbol splitting diversity