Coding for the Fading Channel: a Survey <s> Antenna diversity <s> Since the early 1970s, for power-limited applications, the convolutional code constraint length K=7 and rate 1/2, optimum in the sense of maximum free distance and minimum number of bit errors caused by remerging paths at the free distance, has become the de facto standard for coded digital communication. This was reinforced when punctured versions of this code became the standard for rate 3/4 and 7/8 codes for moderately bandlimited channels. Methods are described for using the same K=7, rate 1/2 convolutional code with signal phase constellations of 8-PSK and 160PSK and quadrature amplitude constellations of 16-QASK, 64-QASK, and 256-QASK to achieve, respectively, 2 and 3, and 2, 4, and 6 b/s/Hz bandwidth efficiencies while providing power efficiency that in most cases is virtually equivalent to that of the best Ungerboeck codes for constraint length 7 or 64 states. This pragmatic approach to all coding applications permits the use of a single basic coder and decoder to achieve respectable coding (power) gains for bandwidth efficiencies from 1 b/s/Hz to 6 b/s/Hz. > <s> BIB001 </s> Coding for the Fading Channel: a Survey <s> Antenna diversity <s> Preface. 1. Fading Channel Modeling. 2. Digital Transmission over Fading Channels. 3. Convolutional Codes. 4. Bandwidth-Efficient Coded-Modulation Schemes. 5. Trellis-Coded Modulation Schemes for Fading Channels. 6. Reed-Solomon Codes. 7. RS-Coded MPSK Schemes for Fading Channels. 8. Differential Detection of Coded-Modulation Schemes on a Fading Channel. 9. Performance of Coded Modulation Schemes on Shadowed Rician Fading Channels. 10. Quadrature Pulse-Overlapping Modulation Techniques. Appendix A: Calculation of the Chernoff Factors for Rician and Rayleigh Fading Channels. Appendix B: Calculation of the Transition Probabilities for the MPSK Signal Set over a Rayleigh Fading Channel. Appendix C: Encoding and Decoding Techniques for RS Codes Using Fourier Transform. Appendix D: Derivation of the Probability of Correct Decision for Reliable and Unreliable MPSK Symbols. References. Index. <s> BIB002 </s> Coding for the Fading Channel: a Survey <s> Antenna 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> BIB003 </s> Coding for the Fading Channel: a Survey <s> Antenna 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> BIB004
PSK modulation M independent diversity branches whose signal-to-noise ratio is inversely proportional to M (this assumption is made in order to disregard the SNR increase that actually occurs when multiple receive elements are used). J4: 4-state, rate-2/3 TCM scheme based on 8-PSK and optimized for Rayleigh-fading channels BIB002 . U4: 4-state rate-2/3 TCM scheme based on 8-PSK and optimized for the Gaussian channel. U8: Same as above, with 8 states. Q64: "Pragmatic" concatenation of the "best" rate-1/2 64-state convolutional code with 4-PSK modulator and Gray mapping BIB001 . Fig. 4 compares the performance of U4 and J4 (two TCM schemes with the same complexity) over a Rayleigh-fading channel with M -branch diversity. It is seen that, as M increases, the performance of U4 comes closer and closer to that of J4. Similar results hold for correlated fading. Even for moderate correlation J4 loses its edge on U4, and for M as low as 4 U4 performs better than J4 BIB003 . The effect of diversity is more marked when the code used is weaker. As an example, two-antenna diversity provides a gain of 10 dB at BER=10 ,6 when U8 is used, and of 2.5 dB when Q64 is used BIB003 . The assumption of branch independence, although important, is not critical. In effect, BIB003 shows that branch correlation coefficients as large as .5 degrade system BER only slightly. The complexity introduced by diversity can be traded for delay. As shown in BIB003 , in some cases diversity makes interleaving less necessary, so that a lower interleaving depth (and consequently a lower overall delay) can be compensated by an increase of M . When differential or pilot-tone, rather than coherent, detection is used BIB004 , a BER-floor occurs which can be reduced by introducing diversity. As for the effect of co-channel interference, even its BER-floor is reduced as M increases (although for its elimination multi-user detectors should be employed). This shows that antenna diversity with maximal-ratio combining is highly instrumental in making the fading channel closer to Gaussian. 