Equalization, windowing and zero restoration for OFDM and single-carrier block transmission

Fourier transform (DFT). In the case of MCM, the transmitted data is encoded into blocks in the frequency domain, by using an inverse DFT (IDFT) at the transmitter. The receiver then consists of a DFT, followed by a one-tap complex equalizer for each tone. In SC-FDE the information is encoded into blocks in the time domain. At the receiver, the DFT and one-tap equalizer are followed by an extra IDFT. To avoid the loss of orthogonality between the tones, a guard interval (GI) is inserted between each two blocks. If the channel order doesn?t exceed the GI length, zero-forcing equalization is possible. For longer channels, a Per-Tone equalizer (PTEQ) can be used, which minimizes the mean square error of the received symbols. In practice, the individual bands are orthogonal but overlap, due to the slow roll-off of the DFT?s side lobes. This has an undesirable effect both for the ingress and egress of the signal. Traditionally this problem is solved by applying window functions. Unfortunately, at the transmitter, window functions disturb the orthogonality between the tones. Therefore, a special class of window functions was developed, for which the loss of orthogonality is predictable, such that it can be restored at the receiver. These window functions have a beneficial influence on the egress and make it easier to meet regulatory standards. There is also a need for window functions at the receiver, to avoid the contamination of a whole range of tones by one narrow-band interferer. For short channels, this can be easily done. However, combining window functions and the PTEQ is nontrivial. For two classes of windows, namely the trapezoidally tapered and the raised cosine window, an efficient equalization scheme was developed, combining these windows with the PTEQ. This technique was also patented by an industrial partner. Some channels exhibit one or more spectral zeros, i.e. tones where the channel response is zero or close to zero. For the case of a MCM with feedback from the receiver to the transmitter, it can be decided to discard that tone and not to encode any information on it. For all other cases, the loss of the information which was stored at the spectral zero should be dealt with using some form of coding. For the case of SC-FDE using a zero pad for a GI, we have developed a method to estimate the content of a spectral zero, making use of redundancy in the time domain. This technique was called zerorestoration (ZR) because it allows to restore information which was lost in spectral zeros. Finally, a combination of the PTEQ and ZR was proposed.