# Downsampling of DFT Precoded Signals for the AWGN Channel

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### Abstract

In this paper we propose and analyze a method for downsampling DFT
precoded signals. Since the symbols (in frequency) are in the
constellation set, which is a subset of the entire complex plane, it
is possible to detect N symbols from the DFT precoded signal when
transmitting symbols, where is not too small. We build
our analysis on so-called simple vectors, and show that it is possible
to detect in the noise-less case with high probability down to
approximately for BPSK and for
QPSK. We develop extensions from the noise-less to the noisy case, and
propose two different detectors for the AWGN channel. Simulations show
that using the two proposed detectors in the AWGN channel, we observe
empirically a phase transition at M approximately for
QPSK. Further, it is shown how downsampled QPSK signals can achieve
the same BER and data rate as 8PSK at a lower signal-to-noise-ratio
per information bit.

*Paper published at IEEE International Symposium on Signal Processing
and Information Technology, 2012.*

Matlab scripts neccessary to reproduce the results above are available
below. For help, see README.txt

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4GMCT (VBN)

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