Per-Tone Precoding and Per-Tone Equalization for OFDM and DMT Transmission Systems: Duality, Filter Optimization, and Resource Allocation

OFDM and DMT transmission systems add a cyclic prefix (CP) or zero pad (ZP) to the transmitted signal. Interference-free transmission requires this CP/ZP to be similarly long as the channel impulse response (CIR), reducing the achievable data rate in highly dispersive channels. A first strategy for dealing with long CIRs without increasing the CP/ZP overhead consists of applying a channel shortening filter to the received signal. A second strategy consists of spectral resource allocation, i.e. bit and power allocation to reduce interference. As little effort has been made towards joint channel shortening and resource allocation, a new algorithm to simultaneously optimize the channel shortening per-tone equalization (PTEQ) filters and the resource allocation is presented. In addition, transmitter-side channel shortening filters are considered, more specifically so-called per-tone precoding (PTPC) filters which apply the channel shortening filter before the IDFT modulation of the ODFM/DMT transmitter. At first glance, the FIR filter optimization for PTPC seems much more involved than the relatively straightforward FIR filter optimization for PTEQ. However, it will be demonstrated that any OFDM/DMT system with PTPC is — after time-reversing the CIR — equivalent to an OFDM/DMT system employing PTEQ. With this result in hand, systems with PTPC can take full advantage of the straightforward FIR filter optimization in systems with PTEQ, as well as of the aforementioned resource allocation algorithm. Simulation results show that the performance obtained for systems with PTPC is nearly indistinguishable from that obtained for systems with PTEQ, making PTPC an interesting alternative channel shortening strategy.