WHTDM: Walsh-Hadamard Transform Division Multiplexing for Doubly-Selective Channels

We propose Walsh-Hadamard Transform Division Multiplexing (WHTDM), a multicarrier waveform that replaces the conventional IFFT/FFT pair in OFDM with a real-valued, unitary Walsh-Hadamard transform (WHT). WHTDM inherits the CP-OFDM transceiver structure while eliminating all complex multiplications from the transform stage, yielding a transmitter with zero real multipliers in the core modulation block. For detection under doubly-selective channels, we adopt a cross-domain memory approximate message passing (CD-MAMP) equalizer that operates on the banded structure of the equivalent WHT-domain channel matrix. Simulation results under the 3GPP TDL-C channel model at 28 GHz demonstrate that WHTDM with CD-MAMP significantly outperforms conventional OFDM 1-tap MMSE at high mobility, achieving over an order of magnitude lower BER at 120 km/h. Among the compared CD-MAMP-equalized new waveforms, WHTDM achieves the best BER performance while maintaining a transmitter complexity 2.5 $\times$ lower than OFDM and completely eliminating complex multipliers from the transform stage, making it well-suited for low-power IoT terminals.