Transceivers with decision feedback equalizers - Signal Processing and Optimization for Transceiver Systems - page 632

Example 19.3: Symbol error probability with DFE (cyclic-prefix systems)
We now repeat Ex. 19.2 with cyclic prefixing instead of zero padding. Channel
C 1 ( z ) from Ex. 19.1 is used again (with energy normalized to unity). The
blocksizeistakentobe M =16 . A 2-bit PAM constellation was used. In this
example σ s = 1 as usual, and σ q =0 . 01 . With cyclic prefixing, the equivalent
matrix channel H is a circulant matrix, and it is diagonalized by the DFT matrix.
We can therefore take the matrices V h and U h in Figs. 19.6 and 19.9 to be the
IDFT and DFT matrices (with minor adjustments to account for the fact that
the singular values σ h,k are the magnitudes of the channel DFT coe cients, in
decreasing order). The unitary matrix S in the precoder and the upper triangular
matrix B in the decision feedback loop do not have additional structure because
they are obtained from a QRS decomposition of a general diagonal matrix as in
previous examples.
From the plots of the error probability in Fig. 19.19 we see once again that
DFE leads to substantial improvement in performance. This improvement due to
DFE is much more significant than the improvement that arises from replacing
zero-forced systems with non-zero-forced (pure-MMSE) systems.