Aspects of Coding and Modulation for OFDM

The channel capacity of some ISI channels is examined under the condition that OFDM in conjunction with QAM modulation for subcarriers and the BICM coding scheme is used. The combination of higher order modulation schemes and low rate codes yields results relatively close to the optimum possible solution, even without application of water-filling and/or bit loading. Simulations with a turbo coded OFDM system confirm the results. I.INTRODUCTION OFDM is a method to divide intersymbol interference channels (ISI) into a number of parallel, ISI-free subchannels. When additive white gaussian noise (AWGN) is superimposed, the channel capacity can be achieved by applying the well known “water-filling” theorem [1]. However, it was shown that for fading channels the capacity difference between a “water-filled” (WF) distribution and uniform distribution of the transmit power is relatively small, especially at higher SNRs, and the use of higher order modulation schemes with high rate codes was suggested [2]. Recently, Caire et al. [3] demonstrated that the performance of bit-interleaved coded modulation (BICM) with Gray mapping is relatively close to the optimum for memoryless AWGN channels. Contrary to coded modulation (CM) or multilevel coding (MLC) [4][5], BICM has a simple coder/decoder structure which allows to consider coding and modulation almost separately. An OFDM system represents a number of parallel AWGN subchannels. Therefore, the combination of BICM and OFDM should lead to results relatively close to the optimum. In this paper, we evaluate the channel capacity of BICMOFDM systems without WF for several ISI channels. The maximum possible capacity (e.g. using higher order modulation alphabets together with CM/MLC schemes and waterfilling) is compared to the capacity of BICM-OFDM. Furthermore, the problem of choosing a proper combination of the code rate and the number of bits per modulation symbol at a certain modulation rate is addressed. Simulations with a turbo coded OFDM system confirm the considerations based on capacity. Finally, a comparison to results obtained with single carrier transmission using iterative equalization at the receiver is made [6], and possible applications to the Hiperlan/2 physical layer are presented. Transmission model The transmission model is depicted in fig. 1. It represents an idealized OFDM system using all carriers and is neglecting real-world effects from filter-roll-offs at the borders of the spectrum and around DC. The length channel impulse response is small compared to the number of carriers , . The receiver is assumed to have perfect knowledge of channel and noise power, so after cutting off the cyclic extension and DFT, the estimation values are calculated, being the DFT of ! " . From these values, the corresponding bitmetrics are determined according to (4). Note that in fig. 1, # $&%(' represents the % th bit of the th carrier of the ) th OFDM symbol. II.CHANNEL MODELS Different channels are considered, e.g., the 5-tap minimum distance channel (MD5) with taps 0.29, 0.50, 0.58, 0.50, 0.29 repesenting a “worst case” regarding the path distance in an equalization trellis [7, ch. 10.1]. A second 5 tap channel with similar properties and taps 0.227, 0.46, 0.688, 0.46, 0.227 (referred to as MD5-2 channel) is used for comparison of BICMOFDM with a single carrier / iterative equalization system For Hiperlan, the channel model “C” of [8] is used. III.CAPACITY OF ISI CHANNELS WITH OFDM Using OFDM with a cyclic extension divides the ISI channel into parallel AWGN subchannels. The capacity must be averaged over the subchannels