  Vector orthogonal frequency division multiplexing (V-OFDM) is a general
system that builds a bridge between OFDM and single-carrier frequency domain
equalization in terms of intersymbol interference and receiver complexity. In
this paper, we investigate the sparse multipath channel estimation and decoding
for broadband V-OFDM systems. Unlike the non-sparse channel estimation, sparse
channel estimation only needs to recover the nonzero taps with reduced
complexity. Consider the pilot signals are transmitted through a sparse channel
that has only a few nonzero taps with and without additive white Gaussian
noise, respectively. The exactly and approximately sparse inverse fast Fourier
transform (SIFFT) can be employed for these two cases. The SIFFT-based
algorithm recovers the nonzero channel coefficients and their corresponding
coordinates directly, which is significant to the proposed partial intersection
sphere (PIS) decoding approach. Unlike the maximum likelihood (ML) decoding
that enumerates symbol constellation and estimates the transmitted symbols with
the minimum distance, the PIS decoding first generates the set of possible
transmitted symbols and then chooses the transmitted symbols only from this set
with the minimum distance. The diversity order of the PIS decoding is
determined by not only the number of nonzero taps, but also the coordinates of
nonzero taps, and the bit error rate (BER) is also influenced by vector block
size to some extent but roughly independent of the maximum time delay.
Simulation results indicate that by choosing appropriate sphere radius, the BER
performance of the PIS decoding outperforms the conventional zero-forcing
decoding and minimum mean square error decoding, and approximates to the ML
decoding with the increase of signal-to-noise ratio, but reduces the
computational complexity significantly.
