Performance analysis of QAM in amplify-and-forward cooperative communication networks over Rayleigh fading channels

Performance analysis of quadrature amplitude modulation (QAM) schemes for cooperative amplify-and-forward (AF) dual-hop relaying system over independent and identically distributed (i.i.d.) Rayleigh fading channels are presented in this paper. Specifically, we derive closed-form lower-bound expressions of average symbol error rate (ASER) for general order rectangular QAM (RQAM) and cross QAM (XQAM) using well-known moment generating function (MGF) based approach with maximal ratio combining (MRC) scheme. Further, using best relay selection scheme (BRS), we also derive an ASER expression for XQAM. Numerical and simulated results are compared to validate the correctness of derived expressions. Furthermore, comparative analysis of RQAM and XQAM schemes is discussed which confirms that XQAM is better alternative over RQAM for transmission of odd number of bits per symbol for the considered system model. We also compare the ASER performance for MRC and BRS schemes in terms of SNR gain using different XQAM constellations. Moreover, the impact of system parameters on ASER is also highlighted.     

Suboptimum Viterbi algorithm for trellis-coded QAM scheme inmultipath Rayleigh fading channels

A new suboptimum Viterbi algorithm for trellis-coded quadrature amplitude modulation based on the channel state information of the multipath Rayleigh fading channel is proposed. Simulation results show that the proposed algorithm has merits for applications that require low bit energy-to-noise ratio     

Signaling constellations for fading channels

The performance of various coherent 8-ary and 16-ary modulations in additive white Gaussian noise (AWGN) and slowly fading channels are analyzed. New expressions for the exact symbol error rates (SER) in fading with diversity combining are derived for any two-dimensional signaling format having polygonal decision boundaries. Maximal ratio combining, equal gain combining, and selection combining are considered. The SER formulas obtained make it possible for the first time to optimize parameters of various constellations precisely and to determine,which constellation has the lowest probability of error. For example, a star constellation such as that specified in the CCITT V.29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0.63 dB power in AWGN without sacrificing the phase error tolerance, while maintaining the same error rate. The sensitivity of each constellation to phase error is presented and comparisons are made. Six 8-ary signal sets and 11 16-ary signal sets are examined using the new symbol error probability formulas to determine best signal sets for fading channels     

BER evaluation for general QAM in Nakagami-m fading channels

Evaluation of the bit error rate for general M-ary quadrature amplitude modulation (M-QAM) in Nakagami-m fading channels is presented. The analysis considers real values of the Nakagami fading parameter m, and bit-to-symbol mapping that is not necessarily Gray. Analytical and simulation results are compared to illustrate the accuracy of the analysis, taking as examples non-Gray mapped 16-QAM and 32-cross-QAM constellations.     

Asymptotic performance analysis of arbitrary rectangular QAM over fading channels

In this paper, the asymptotic performance of arbitrary rectangular Quadrature Amplitude Modulation (QAM) signals over fading channels is investigated. A novel unified asymptotic average Symbol Error Probability (SEP) expression is derived in terms of diversity and coding gain. The validity and accu-racy of the analytical result are verified by means of computer simulations. Furthermore, the results pre-sented are very easy to be extended to the systems with multi-channel diversity receivers.     

Design and performance of BICM-ID systems with hypercube constellations

This paper introduces new mappings of QPSK symbols, viewed as a multi-dimensional hypercube, to improve the performance of bit-interleaved coded modulation with iterative decoding (BICM-ID). By evaluating the upper bound of the bit error rate performance of BICM-ID, a condition to find the best mapping of a hypercube constellation in terms of the asymptotic performance under different channel models is established. A general and simple algorithm to construct the best mapping of a hypercube is then proposed. Analytical and simulation results show that the use of the proposed mappings together with very simple convolutional codes can offer significant coding gains over the conventional BICM-ID systems for all the channel models considered. Such coding gains are achieved without bandwidth or power expansion and with a very small increase in the system complexity.     

V-BLAST without optimal ordering: analytical performance evaluation for Rayleigh fading channels

The Bell Labs layered space-time (BLAST) algorithm is simple, and hence, a popular choice for a multiple-input multiple-output (MIMO) receiver. Its bit-error rate (BER) performance has been studied mainly using numerical (Monte Carlo) techniques, since exact analytical evaluation presents serious difficulties. Close examination of the problem of BLAST BER performance analysis reveals that the major difficulty for analytical evaluation is due to the optimal ordering procedure. Hence, we analyze the algorithm performance without optimal ordering. While this is a disadvantage of the analysis, there are certain advantages as well. Exact closed-form analytical evaluation is possible for arbitrary number of transmit and receive antennas in an independent, identically distributed Rayleigh fading channel, which provides deep insight and understanding that cannot be gained using the Monte Carlo approach alone. A result on the maximum ratio combining weights, which is used at each detection step, is derived to obtain a number of results: independence of noise, distribution of signal-to-noise ratio (SNR), and block- or bit-error rates. We present a detailed analysis and expressions for uncoded error rates at each detection step, which hold true for any modulation format and take simple closed form in some cases. Asymptotic form of these expressions for large SNRs is particularly simple. Extensive Monte Carlo simulations validate the analytical results and conclusions.     

Simplified eIRA code design and performance analysis for correlated Rayleigh fading channels

We present a simple design technique for extended irregular repeat-accumulate (eIRA) codes for flat Rayleigh fading channels, using simple channels as surrogates in the design. We show that eIRA codes designed for the burst-erasure channel (BuEC) or the burst-erasure channel with AWGN (BuEC-G) achieve essentially the same performance over Rayleigh fading channels as codes designed for the fading channel. Thus, to design good codes for Rayleigh fading channels, instead of implementing the complex design procedures targeted, specifically for this channel, we propose the simple approach of designing codes over surrogate channels, the BuEC or the BuEC-G. We also show that eIRA codes designed for the BuEC enjoy the advantage of efficient encodability and a lower error-rate floor. Finally, we demonstrate that it is the distribution of the number of faded bits per codeword which determines the difference between correlated and uncorrelated fading channel performance. Perfect channel state information is assumed in this paper.     

Good lattice constellations for both Rayleigh fading and Gaussianchannels

Recent work on lattices matched to the Rayleigh fading channel has shown how to construct good signal constellations with high spectral efficiency. We present a new family of lattice constellations, based on complex algebraic number fields, which have good performance on Rayleigh fading channels. Some of these lattices also present a reasonable packing density and thus may be used at the same time over a Gaussian channel. Conversely, we show that particular versions of the best lattice packings (D₄, E₆, E₈, K₁₂ , Λ₁₆, Λ₂₄), constructed from totally complex algebraic cyclotomic fields, present better performance over the Rayleigh fading channel. The practical interest in such signal constellations rises from the need to transmit information at high rates over both terrestrial and satellite links. Some further results in algebraic number theory related to ideals and their factorization are presented and the decoding algorithm used with these lattice constellations are illustrated together with practical results     

Design and analysis of turbo codes on Rayleigh fading channels

The performance and design of turbo codes using coherent BPSK signaling on the Rayleigh fading channel is considered. In low signal-to-noise regions, performance analysis uses simulations of typical turbo coding systems. For higher signal-to-noise regions beyond simulation capabilities, an average upper bound is used in which the average is over all possible interleaving schemes. Fully interleaved and exponentially correlated Rayleigh channels are explored. Furthermore, the design issues relevant to turbo codes are examined for the correlated fading channel. Turbo interleaver design criteria are developed and architectural modifications are proposed for improved performance     

Unified analysis of error performance for binary signalling over Rayleigh fading channels

Using the unified expression as devised by Wojner, an analytical framework is presented to determine error performance of all binary modulation schemes employing coherent or non-coherent detection and operating over a slow flat Rayleigh fading channel with different diversity combining. A class of generalised expressions for the bit error probability has been obtained following the probability density function or the cumulative distribution function approach.     

Exact performance analysis of M-ary QAM with MRC diversity in Rician fading channels

The exact expression of symbol error rate (SER) is derived for coherent square M-ary quadrature amplitude modulation (M-QAM) using Lth order maximal-ratio combining (MRC) diversity in Rician fading channels with an arbitrary fading parameter. The accuracy of the SER estimates evaluated by this expression is verified through comparison with the results evaluated by numerical integration.     

Effects of multipath diversity on adaptive QAM in frequency selective Rayleigh fading channels

We derive the average bit error rate (BER) and the average throughput for adaptive quadrature amplitude modulation (AQAM) with constant transmit power over frequency selective Rayleigh fading channels. Based on these derived BER and throughput expressions, we go on to investigate the effect of multipath diversity on AQAM using two BER constraints.     

Exact analysis for downlink MC-CDMA in Rayleigh fading channels

In this letter, downlink multicarrier code-division multiple access (MC-CDMA) systems with maximal ratio combining (MRC) in frequency-selective Rayleigh fading channels is considered. An exact bit error rate (BER) is provided based on the characteristic function (CF) and residue calculation method. The BER performance is evaluated in the time domain instead of the frequency domain. This method does not require any assumption regarding the statistical or spectral behavior of multiple access interference (MAI).     

Rayleigh fading compensation for QAM in land mobile radiocommunications

A pilot symbol-aided Rayleigh fading compensation is investigated for M-ary quadrature amplitude modulation (QAM) to achieve highly spectrally efficient land mobile communication systems. The optimum parameters for fading compensation, bit error rate (BER) performance against E_b/N₀ (energy per bit to the noise power spectrum density), adjacent channel interference, and cochannel interference for 16-QAM, 64-QAM, and 256-QAM, and the spectral efficiencies for these modulation schemes in Rayleigh fading environments are investigated by computer simulation. To further verify the effect of pilot symbol-aided fading compensation from a a practical point of view, a 16-QAM modem is implemented, laboratory experiments are executed, and the impact of the dynamic range limitation due to the resolution of the analog-to-digital (A/D) converters is evaluated, along with the imperfection of the analog circuits. It is demonstrated by computer simulation and laboratory experiments that the pilot symbol-aided fading compensation can sufficiently compensate for fast varying Rayleigh fading, and 16-QAM gives the highest spectral efficiency in the case of cellular systems     

An MGF-based performance analysis of generalized selectioncombining over Rayleigh fading channels

Using the notion of the “spacing” between ordered exponential random variables, a performance analysis of the generalized selection combining (GSC) diversity scheme over Rayleigh fading channels is presented and compared with that of the conventional maximal-ratio combining and selection combining schemes. Starting with the moment generating function (MGF) of the GSC output signal-to-noise ratio (SNR), we derive closed-form expressions for the average combined SNR, outage probability, and average error probability of a wide variety of modulation schemes operating over independently, identically distributed (i.i.d.) diversity paths. Because of their simple form, these expressions readily allow numerical evaluation for cases of practical interest. The results are also extended to the case of non-i.i.d. diversity paths     

Design of trellis coded QAM for flat fading and AWGN channels

The design of trellis coded modulation (TCM) schemes for QAM constellations to counteract simultaneous flat fading and additive white Gaussian noise (AWGN) is considered. Motivated by the results of Divsalar and Simon (see IEEE Trans. Commun., vol.36, p.1004, 1988), and incorporating some recent ideas from Boulle and Belfiore (1992), we develop novel 2-D TCM schemes that attain diversity of order two even for a trellis structure that includes parallel paths with one symbol per edge. An algorithm is described that transforms codes designed for the AWGN channel into codes that achieve significant gains over flat fading channel, while preserving their coding gain over AWGN channel. Their performance is assessed via computer simulation for some representative TCM-QAM schemes under the assumption of uncorrelated fading and perfect channel state information (CSI). Finally, the effects of finite interleaving as well as imperfect CSI on code performance are investigated     

Error analysis for nonuniform signaling over Rayleigh fading channels

We investigate the error performance of a communication system where a nonuniform memoryless binary source is transmitted via Gray-mapped M-ary phase-shift keying or quadrature amplitude modulation over memoryless Rayleigh fading channels, and demodulated via optimal maximum a posteriori detection. Using recently derived upper and lower bounds on the probability of a general union of events, which are tight and can be efficiently computed, the system symbol-error (P/sub s/) and bit-error (P/sub b/) rates are evaluated for a wide range of channel conditions. Since for nonuniform signaling, Gray mapping is not necessarily optimal for minimizing P/sub s/ or P/sub b/ (as was recently shown by Takahara et al.), we also evaluate the system performance under the map obtained by Takahara et al. and compare it with a Gray-mapped system.     

Capacity evaluation for equal gain diversity schemes over Rayleigh fading channels

In this paper, closed-form expressions for the capacities per unit bandwidth for Rayleigh fading channels with equal gain combining (EGC) diversity case are derived for power and rate adaptation, constant transmit power, channel inversion with fixed rate, and truncated channel inversion adaptation policies. Channel inversion policies provide the highest capacity over the other adaptation policies with EGC diversity. The constant transmit power policy provides the lowest capacity as compared to the other policies.