  Orthogonal frequency division multiplexing (OFDM) is a modulation technique
susceptible to source, channel and amplifier nonlinearities because of its high
peak-to-average ratio (PAPR). The distortion gets worse by increasing the
average power of the OFDM signals since larger portion of the signals are
affected by nonlinearity. In this paper we introduce Hadamard coded modulation
(HCM) that uses the fast Walsh-Hadamard transform (FWHT) to modulate data as an
alternative technique to OFDM in direct-detection wireless optical systems.
This technique is shown to have a better performance for high average optical
power scenarios because of its small PAPR, and can be used instead of OFDM in
two scenarios: 1) in optical systems that require high average optical powers
such as visible light communications (VLC), and 2) in optical wireless systems
unconstrained by average power, for which HCM achieves lower bit error rate
(BER) compared to OFDM. The power efficiency of HCM can be improved by removing
a part of the signal's DC bias without losing any information. In this way, the
amplitude of the transmitted signal is decreased and the signals become less
susceptible to nonlinearity. Interleaving can be applied on HCM to make the
resulting signals resistent against inter-symbol interference (ISI) effects in
dispersive channels by uniformly distributing the interference over all
symbols.
