In this paper we propose and analyze a method for downsampling discrete Fourier transform (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 M < N symbols, whereM 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 ≥ N/4 for BPSK and M ≥ 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 ≈ 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.
Proceedings of the 12th Ieee International Symposium on Signal Processing and Information Technology, 2012, p. 141-146
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IEEE International Symposium on Signal Processing and Information Technology, 2012