A Communication System Based on Walsh–Hadamard Codes and Constellations for Fading Environments

Optimum detection of Walsh-Hadamard multiplexed antipodal signals over Rayleigh fading channels

“…The transmitter of the system is identical to the one used in [4] and [5]. However, different notation is used in order to analyze the system in a more convenient matrix/vector form.…”

“…This detector, which was developed and analysed in [4][5], consists of two parts: a MAP detector which decides on a symbol-bysymbol basis about the received channel symbols; a WalshHadamard demultiplexer that recovers the transmitted information symbols.…”

“…Finally, demultiplexing of the channel symbols to information symbols may be easily achieved as described in [4] and is mathematically equivalent to matrix multiplication over each block of M channel symbols, i.e.…”

“…[1][2], or as an M−ary modulation technique in 3G cdma2000 systems [3]. Recently, a coded modulation or multiplexing scheme based on Walsh-Hadamard codes was described and analyzed [4]. Antipodal information symbols are spread by different Walsh codes which are then summed up over the block (length of the code) level prior to transmission.…”

“…Based on the approach of [4], and restricting our attention to simple rectangular produced constellations, a MAP vector detector is analyzed in this paper. The bit error probability (BEP) of the system is computed either by simulation or by upper and lower bounds analytically or numerically derived.…”