LDPC-coded adaptive modulation on slowly varying Nakagami-fading channels

Adaptive coded modulation is a promising idea for bandwidth-efficient transmission on time-varying, narrowband wireless channels. On power limited Additive White Gaussian Noise (AWGN) channels, lowdensity parity-check (LDPC) codes are a class of errorcontrol codes which have demonstrated impressive errorcorrecting qualities, under some conditions performing even better than turbo codes. We propose a combination of these two principles: A rate-adaptive LDPC-coded modulation scheme designed for slowly varying flat fading channels. The scheme’s theoretical performance is evaluated by calculating its bandwidth efficiency for a given target bit error rate (BER) on channels with Nakagami Multipath Fading. Finally we extend the scheme to a potentially zero-error hybrid FEC-ARQ system, without degrading bandwidth efficiency. 1 INCREASING WIRELESS SPECTRAL EFFICIENCY BY LINK ADAPTATION Future generations of wireless communication systems will have to include some form of link adaptation, i.e., rate-adaptive transmission schemes, in order to increase the throughput of information to the levels demanded by high-quality multimedia services. This is because wireless and mobile channels exhibit time-varying channel signal-to-noise ratio (CSNR), usually caused by multipath reflections, shadowing, and the relative movement between transmitter and receiver in a mobile system. Upcoming Wireless Local Area Network (WLAN) standards such as HiperLAN/2 are already beginning to explore link adaptation as a means towards increased spectral efficiency, by means of punctured convolutional codes and QAM modulation [1]. One variant of the link adaptation idea is to use constant power transmission, but to allow for on-line adaptation of channel coding and modulation in such a way that highly bandwidth efficient multilevel coding is used when the CSNR is high, and less bandwidth efficient coding (more redundancy) is used when the CSNR is low. This assumes that the transmitter has access to the channel state information (CSI) at any time. For slowly varying frequency-flat channels (those with limited mobility and thus limited Doppler shifts, and with limited time dispersion) the CSNR is the same at all frequencies and can also be regarded as nearly constant for shorter periods of time (less than the coherence time). This makes it possible to feed back relevant CSI to the transmitter using a feedback or return channel. During a time interval of length less than the coherence time the channel can now be well approximated by an AWGN channel. An efficient transmission scheme designed for an AWGN channel with the same stationary signal-to-noise ratio will therefore be a good scheme for a wireless channel, as long as the channel is frequencynonselective and the scheme does not require processing of blocks longer than the channel coherence time. When choosing the individual channel codes employed in an adaptive scheme, one should therefore ensure that each code has satisfactory performance on an AWGN channel within some certain CSNR range. One could say that the principle of adaptive coded modulation effectively reduces a time-varying channel to a ”bank” of temporally multiplexed AWGN channels, each of which is to be used to represent some finite (small) interval on the CSNR axis. This is beneficial since the search for good codes on AWGN channels is a problem which has been subject to much research and large breakthroughs in the last decade. 2 THE FLAT FADING CHANNEL MODEL The flat-fading channel is a much-used model for narrowband transmission over wireless and mobile communication channels, and the one to be used here. On a flat-fading channel, all signal frequencies are attenuated by the same factor. In a broadband wireless system the channel is frequency-selective, but the flat-fading model may still be used to model one subchannel if multicarrier (OFDM) modulation is used, such as is the case e.g., for HiperLAN/2. The received signal on a flat-fading channel can be written at a given time instant in the complex baseband domain as (1) where is the fading amplitude, is the transmitted channel symbol (in general complex), and is complex AWGN. The fading amplitude is also in general complex, but may be assumed to be real-valued if perfect coherent detection is assumed at the receiver end. We shall adopt this commonly used assumption throughout this paper. The fading amplitude (for notational simplicity we suppress the time dependence from now on) can be described as a stochastic variable, whose distribution we shall assume to be known. One particularly interesting distribution is the Nakagami distribution [2]: