Arbitrary Rectangular Quadrature Amplitude Modulation Research Articles

Error-Rate Analysis of OFDM Radio Link Over Mobile Rayleigh Channel Under Multiple RF Impairments

In this paper, we analyze the sensitivity of orthogonal frequency-division multiplexing waveforms to the joint distortion effects of coexisting nonidealities in the implementation of transceiver radio frequency (RF) electronics, combined also with time variations of the multipath radio channel. To cope with the challenge in evaluation of error rates under non-Gaussian joint interference, we propose a semianalytical method for the evaluation of the uncoded symbol-error rate for an arbitrary rectangular quadrature amplitude modulation as subcarrier modulation. This allows deriving maximum tolerable impairment levels for RF circuits such that the link detection error rate is kept at a target level.

Exact and Closed-Form Error Performance Analysis for Hard MMSE-SIC Detection in MIMO Systems

We investigate the exact error performance of hard minimum mean-squared error (MMSE) detection possibly with successive interference cancellation (SIC) in multiple-input multiple-output (MIMO) systems. To facilitate the analysis, we start with an exact bit-error rate (BER) analysis for a general system with decision statistic, z=ax+u, where a>;0, x is the transmitted signal, and u is an arbitrarily distributed noise component which is possibly dependent on the signal component x. For this general system, we derive the exact and closed-form BER expressions for M-ary pulse amplitude modulation (PAM) and arbitrary rectangular quadrature amplitude modulation (QAM), which include the well-known BER result of as a special case. Furthermore, by formulating the MIMO MMSE decision statistics in the same form as z in the general system, we derive the exact and closed-form instantaneous BER and symbol-error rate (SER) expressions for MIMO hard MMSE detection with/without SIC employing PAM and QAM. Finally, the validity of our derived error probability expressions is verified through extensive Monte Carlo simulations and the results reported in the literature.

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 accuracy of the analytical result are verified by means of computer simulations. Furthermore, the results presented are very easy to be extended to the systems with multi-channel diversity receivers.

Impact of delayed arbitrary transmit antenna selection on the performance of rectangular QAM with receive MRC in fading channels

Constrained switching rate imposes practical limitations on the effectiveness of selection combining diversity algorithms. This paper investigates the impact of delayed arbitrarily ordered transmit antenna selection on the average symbol error probability (SEP) performance of arbitrary rectangular quadrature amplitude modulation (QAM) with receive maximal ratio combining (MRC) diversity. New closed form expression is presented for the system average SEP considering the case of statistically independent diversity branches over which the instantaneous fading-to-noise power ratios follow Gamma distributions.

Performance of W-CDMA systems with rectangular signalling in OSTBC MIMO generalised Nakagami-m fading channels

The performance of combined temporal multipath diversity with statistically independent branches and spatial antenna diversity with arbitrarily correlated branches is investigated. A downlink wide-band code-division multiple access system employing orthogonal space-time block coding multiple-input-multiple-output communications is considered. The performance is quantified in terms of the average symbol error probability (SEP) of coherent arbitrary rectangular quadrature amplitude modulation in Nakagami-m fading with arbitrary statistics. Through the analysis, new expressions for the average SEP are derived under the generalised system model described above. Specifically, the considerations of the combined path and space diversity model, the arbitrary correlation profile among spatial diversity branches, and the arbitrary statistics of Nakagami-m fading processes are the main aspects that make the system model herein generalised as compared to previous ones. Furthermore, for this generalised system model, the consideration of distinct in-phase and quadrature decision distances as well as modulation orders in the rectangular signalling constellation through the analysis provide additional enhancements on some existing results. Numerical and simulation results are presented to demonstrate the enhanced validity of the analytical development.

Exact error probability analysis of rectangular QAM for single- and multichannel reception in nakagami-m fading channels

In this contribution, we derive exact closed-form expressions for the average symbol error probability (SEP) of arbitrary rectangular quadrature amplitude modulation (QAM) for single- and multichannel diversity reception over independent but not-necessarily identically distributed Nakagami-m fading channels. The diversity branches may hence exhibit identical or distinctive power levels and their associated Nakagami indexes need not be the same. Our work extends previous results pertaining to nondiversity reception of M-ary rectangular QAM over Rayleigh fading channels and multichannel reception of M-ary square QAM over Nakagami-m fading channels. For a given number L of diversity branches and a corresponding set of arbitrary real-valued Nakagami indexes not less than 1/2, our SEP results are expressed in terms of Gauss's hypergeometric function <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and Lauricella's multivariate hypergeometric function F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L)</sup> of L variables, both of which can be efficiently evaluated using standard numerical softwares.

Average symbol error probability of arbitrary rectangular quadrature amplitude modulation in generalised shadowed fading channels

A closed-form approximation of average symbol error probability of arbitrary rectangular quadrature amplitude modulation in a gamma-shadowed Nakagami fading radio channel is derived. The final result is obtained on the basis of an exponential approximation of the Gaussian Q-function. It is shown that the derived formula can also be used for error probability estimation in Nakagami-log-normal radio channels for a wide range of shadowing spread values. The numerical aspects of calculation are discussed.

Performance analysis of rectangular quadrature amplitude modulation with combined arbitrary transmit antenna selection and receive maximal ratio combining in Nakagami-m fading

The average symbol error probability (SEP) performance of arbitrary rectangular quadrature amplitude modulation in the context of arbitrarily ordered transmit antenna selection and receive maximal ratio combining diversity system is analysed. The channel gains are assumed to follow Nakagami-m fading distribution with in general arbitrary fading parameters. Exact expressions for the average SEP performance are derived for the general case of unequal in-phase and quadrature decision distances as well as distinct in-phase and quadrature modulation orders. The results generalise many previous case studies, and can be used to investigate the impact of various diversity-combining schemes and different modulation and channel parameters on the system average SEP performance.

MRC reception of rectangular M-ary QAM signals over frequency-flat Rayleigh fading channels with distinctive branch fading amplitudes

The usual approach to calculate the symbol error rate (SER) for multilevel (M-ary) signalling over a fading channel is to first find the average SER in an additive white Gaussian noise channel conditioned on a fixed fading parameter and then average this SER over the fading parameter (averaging over the fading parameter at the last stage). This usual approach is called the postaveraging method. A different approach, called the preaveraging method, that is the averaging over the fading parameter is performed on the probability density function of per symbol estimate error in an earlier stage of the derivation process. By doing so, it is possible to obtain an exact closed-form expression of SER for the special case of maximal ratio combining reception of arbitrary rectangular M-ary quadrature amplitude modulation (QAM) signalling over frequency-flat Rayleigh fading channels, which has not been obtained using the usual postaveraging method. For the case under study, it is assumed that all diversity channels have independent, but distinctive, fading amplitudes. The SER results can be applied to any M-size rectangular QAM constellation. The method can be readily extended to square M-ary QAM, M-ary pulse amplitude modulation (PAM) and binary antipodal signalling. It is thought that this method and the closed-form SER result have never been treated and exposed elsewhere for the arbitrary rectangular QAM case under consideration. Monte Carlo simulations prove to be in excellent agreement with the theoretical results.

General bit error probability of rectangular quadrature amplitude modulation

A general closed-form expression of the exact bit error rate (BER) for an arbitrary rectangular quadrature amplitude modulation (R-QAM) with Gray code mapping is derived and analysed under an additive white Gaussian noise channel. A discussion of BER performance for maximum ratio combining diversity in Nakagami fading is also presented.