However, decreasing the reshaping filter length also reduces the equalization performance with respect to the true RIRs, resulting in a trade-off between equalization performance for perfectly estimated RIRs and robustness in the presence of RIR perturbations.
Our earlier study [7] details these physical layers aspects of the noise-OFDM waveform with respect to spectral equalization, noise-like properties, reliability, and covertness.
Further, the iteration of the synchronization and equalization stages also improves the BER, especially with respect to.
Therefore, deriving bound on BER for fast minimization with respect to the equalizer coefficients can still yield powerful and real-time channel equalization.
The conditional expectation of the mean square error is minimized with respect to precoding matrix and equalization coefficient.
The use of widely linear MMSE-designed equalization and precoding brings an error performance advantage with respect to strictly linear systems when improper constellations are transmitted, due to the complete use of the second-order statistics made available by these constellations.
With respect to SC-FDE systems using MMSE-DFE equalization, together with the performance gain, the use of widely linear processing also makes the error performance less sensitive to the feedback filter size.
We can verify that the two FBMC structures, which are equivalent in the flat channel, perform differently on multipath channel because of the difference between the equalization mechanisms; more specifically, the frequency-spreading structure provides improved performance with respect to the standard structure and this improvement increases as the overlapping factor increases.
In this section we numerically investigate the BER with respect to SNR and we also analyze the convergence properties of the equalization algorithms.
We then focus on four specific applications, where the training sequence can be optimized with respect to the classical channel estimation MSE, a weighted channel estimation MSE and the MSE of the equalization error due to the use of an equalizer at the receiver or an appropriate linear precoder at the transmitter.
