# 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 $M$ 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 $M \le N/4$ for BPSK and $M \le N/2$ 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 $N/2$ 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