Coding for the Fading Channel: a Survey <s> Diversity <s> We address the problem of designing and analyzing the performance of a coded modulation scheme for the fading channel when space diversity is used. Under fairly general conditions, a channel affected by fading can be turned into an additive white Gaussian noise (AWGN) channel by increasing the number of diversity branches. Consequently, it can be expected (and is indeed verified by our analyses and simulations) that a coded modulation scheme designed to be optimal for the AWGN channel also will perform asymptotically well on a fading channel with diversity. This paper presents bounds on the bit-error probability of a system with coded modulation and diversity for space- and time-correlated Rician flat fading. Specifically, we derive a new method which allows evaluation of the pairwise error probability extremely easily, as well as accurately and computationally fast. The accuracy achieved improves considerably on the widely used, but rather loose Chernoff bound. Starting from this analysis, we study the asymptotic behavior of the fading channel with diversity as the number of diversity branches increases, and we address the effects of diversity on coded modulation performance and design criteria, including the effect on interleaver depth (which affects the total delay of the system). <s> BIB001 </s> Coding for the Fading Channel: a Survey <s> Diversity <s> For pt. I see ibid., vol.45, no.6, p.563-572, 1997. We study coded modulation with block differential detection in an arbitrarily correlated Rician fading channel with space diversity. Coded differential q-PSK is included in our analysis as a special case. A metric is chosen that is optimum for perfect interleaving, slow fading, and independent diversity branches. For slow fading, we compare the the cutoff rates of the channels resulting from different choices of block length N and diversity index M. Specifically, we show that block detection with diversity may or may not generate a better coding channel than usual differential detection, according to the code selected and the combination of values of M and N. In particular, for low-diversity orders (M=1,2) and for low-to-medium code rates, differential detection is still an optimal or near-optimal solution, while for high-diversity orders (M/spl ges/2) and medium-to-high code rates (up to uncoded modulation) block detection with N>2 can provide a significant gain. An error floor always exists when fading is fast. It decreases exponentially with the product of code diversity and space diversity, so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading. Performance examples based on actual coding schemes are also shown. <s> BIB002 </s> Coding for the Fading Channel: a Survey <s> Diversity <s> For pt.II see ibid., vol.45, no.6, p.55-67, 1997. In previous work, we have studied the impact of diversity on coded digital communication systems operating over fading channels. In particular, we have shown that diversity may be thought of as a way of making the channel more similar to a Gaussian one. The present paper extends this analysis to fading channels affected by co-channel interference (CCI). Three receiver models are examined, namely, with coherent detection and perfect channel-state information (CSI), with differential; and with pilot-tone detection. We study the effect of diversity on the irreducible error floor caused by CCI and fading, and the asymptotic behavior of the channel as the diversity order increases. Our results show that, when perfect CSI is available, diversity is able to turn asymptotically the channel into a CCI-free additive white Gaussian noise (AWGN) channel with the same signal-to-noise ratio (SNR). On the other hand, differential and pilot-tone detection do not remove interference in the limit. Nevertheless, also with these detection schemes, diversity achieves significant gains when the SNR is large enough. Calculation of the channel cutoff rate provides guidelines for the design of coded systems with CCI in fading environments. A wide range of examples, validated by computer simulation, illustrates our conclusions. <s> BIB003 </s> Coding for the Fading Channel: a Survey <s> Diversity <s> The main focus of this presentation is adaptive down-link beam forming for PSK modulation based on subspace decomposition. A down-link beam forming algorithm with reasonable complexity is proposed which requires neither detection of other users' signals nor knowledge about the direction-of-arrival (DOA)s of the incident path components. The desired signal subspace is extracted from the composite space in cooperation with the optimal beam forming for uplink signal reception. <s> BIB004 </s> Coding for the Fading Channel: a Survey <s> Diversity <s> This paper presents code design principles and gives some example codes for high performance transmitter diversity systems in frequency nonselective Rayleigh fading. Transmitter diversity is a good way to achieve diversity on any forward link (i.e. infrastructure to mobile) and is often employed when low mobility could be encountered (e.g. PCS or fixed wireless telephony). An accurate model for the sampled output of the matched filter in narrowband wireless transmission using transmitter diversity is examined. <s> BIB005 </s> Coding for the Fading Channel: a Survey <s> Diversity <s> We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Here, data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals. We derive performance criteria for designing channel codes under the assumption that the fading is slow and frequency non-selective. Performance is shown to be determined by diversity gain quantified by ranks and coding gain quantified by determinants of certain matrices that are constructed from the code sequences. <s> BIB006 </s> Coding for the Fading Channel: a Survey <s> Diversity <s> We revisit space-time codes for a mobile communication system that employs multiple antennas at the base station and optional antenna diversity at the mobile station. The realistic case when the channel state is not completely known is considered. It is assumed that the channel estimator extracts the fade coefficients using orthogonal pilot tones. Mismatch analysis is then carried out. It is proved that in the absence of ideal channel state information the design criteria for space-time codes developed in Tarokh et al. (1997) is still valid for the equal energy constellation case. Using our derivation, it is observed that channel estimation techniques commonly used over rapidly fading channels can be used in conjunction with space-time codes provided that the number of transmit antennas is small. <s> BIB007 </s> Coding for the Fading Channel: a Survey <s> Diversity <s> We study the synergy between coded modulation and antenna-diversity reception on channels affected by slow Rician fading. Specifically, we assess the impact of channel-state information (CSI) on error probability. We show that with a good coding and constant envelope modulations (for example, phase-shift keying) scheme the loss in performance when CSI is not available is moderate (around 1.5 dB). Moreover, as the diversity order grows, the channel tends to become Gaussian. <s> BIB008
Receiver-diversity techniques have been known for a long time to improve the fading-channel quality. Recently, their synergy with coding has been extensively investigated in BIB001 BIB002 BIB003 . The standard approach to antenna diversity is based on the fact that, with several diversity branches, the probability that the signal will be simultaneously faded on all branches can be made small. The approach taken in BIB008 BIB001 BIB002 BIB003 is philosophically different, as it is based upon the observation that, under fairly general conditions, a channel affected by fading can be turned into an additive white Gaussian noise (AWGN) channel by increasing the number of diversity branches. Consequently, it can be expected (and it was indeed verified by analyses and simulations) that a coded modulation scheme designed to be optimal for the AWGN channel will perform asymptotically well also on a fading channel with diversity, at the only cost of an increased receiver complexity. An advantage of this solution is its robustness, since changes in the physical channel affect the reception very little. This allows us to argue that the use of "Gaussian" codes along with diversity reception provides a solution to the problem of designing robust coding schemes for the mobile radio channel. Recently, a considerable amount of work has been presented on transmitter diversity with coding BIB004 BIB005  BIB006 BIB007 . Transmitter diversity may be a viable solution for the downlink of a TDMA system, where the receiver is constrained to be small and light (so that use of multiple antennas is out of the question).