A system includes a differential demodulation module that differentially demodulates modulated signals received from R antennas. A first summing module sums the differentially demodulated signals to generate a combined signal. A state detection module detects states of X symbols in the combined signal. A second summing module (i) receives Y preamble sequences each comprising X predetermined symbols and (ii) generates X sums for each of the Y preamble sequences by adding each of the states of the X symbols with corresponding states of the X predetermined symbols of each of Y preamble sequences. The states of the X predetermined symbols are generated by inverting states of derived symbols in derived preamble sequences, which are derived from the Y preamble sequences. Each of the Y preamble sequences is different from others of the Y preamble sequences. R, X, and Y are integers greater than 1.