Multilevel Codes for OFDM-Like Modulation over Underspread Fading Channels
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Multilevel Codes for OFDM-Like Modulation over Underspread Fading Channels Siddhartha Mallik and Ralf Koetter The Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Received 7 June 2005; Revised 3 May 2006; Accepted 12 May 2006 We study the problem of modulation and coding for doubly dispersive, that is, time and frequency selective, fading channels. Using the recent result that underspread linear systems are approximately diagonalized by biorthogonal Weyl-Heisenberg bases, we arrive at a canonical formulation of modulation and code design. For coherent reception with maximum-likelihood decoding, we derive the code design criteria as a function of the channel’s scattering function. We use ideas from generalized concatenation to design multilevel codes for this canonical channel model. These codes are based on partitioning a constellation carved out from the integer lattice. Utilizing the block fading interpretation of the doubly dispersive channel, we adapt these partitioning techniques to the richness of the channel. We derive an algebraic framework which enables us to partition in arbitrarily large dimensions. Copyright © 2006 S. Mallik and R. Koetter. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
The design of reliable, high data rate mobile wireless communications systems has been an area of tremendous research activity for the last couple of years. New developments in the field of channel modeling, signaling, and code design have enabled technologies that support high data rates in a wireless setting which in turn have fueled consumer interest in adoption and utilization of wireless devices and services. This paper deals with communication over rapidly timevarying channels, that is, channels which cannot be regarded as time-invariant over a frame. In a typical wireless setting, a signal sent from the transmitter reaches the receiver through multiple paths, collectively termed as multipath. Interference among the multiple paths results in a decrease in signal amplitude. Further due to the time-varying nature of the medium, the received signal amplitude varies with time, in other words, the signal undergoes fading. The primary means of combating fading is through diversity, in which copies of the transmitted message are made available on different dimensions (time, frequency, or space) to the receiver. All wireless communications schemes utilize temporal diversity by using sophisticated channel coding in conjunction with interleaving to provide replicas of the transmitted signal in the temporal domain. Frequency diversity techniques employ the fact that waves transmitted on different frequencies induce different multipath structure in the
propagation media. In space or antenna diversity spatially separate antennas are used at the transmitter or the receiver or both. Communication schem
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