Regular paperOn the ASER performance of SC receiver with RQAM and HQAM over - fading
Introduction
In modern wireless communication systems, the family of quadrature amplitude modulations (QAMs) has drawn attention among various modulation schemes due to its potential for providing high data rates, power efficiency, and bandwidth efficiency. The specifications in the 3rd generation partnership project (3GPP) Release-14 (LTE-advanced) and Release-15 (5G-New radio) have also recommended the use of higher order QAM (-QAM and -QAM) for various high data rate applications [1]. The rectangular QAM (RQAM) is a generalized modulation scheme and various modulation schemes such as square QAM (SQAM), binary phase shift keying (BPSK), quadrature phase shift keying (QPSK) and orthogonal binary frequency shift keying can be studied as special cases of RQAM [2], [3]. RQAM scheme has also been employed in microwave communication systems, high speed mobile communication systems and telephone line modems [3]. However, the need for an optimum QAM constellation has drawn the attention of researchers toward the hexagonal lattice based QAMs referred to as hexagonal QAM (HQAM). HQAM is more energy-efficient than SQAM due to the compact packing of constellation points with optimum Euclidean distance [4], [5], [6]. HQAMs also find application in multi-carrier systems, multiple input multiple output systems, optical and wireless communication systems.
In wireless communication systems, the characterization of signal multi-path fading and shadowing has always been of importance. The measurements of short-term fading in both indoor and outdoor environments provide invaluable insight into spatial and temporal fading of multipath amplitudes [7]. The authors in [8] characterized the short-term fading channel in terms of its higher-order statistics for an indoor environment in the millimeter-wave band. Several fading models such as Rayleigh, Rice, Nakagami-, -, -, -, and --- were tested against the measurement data. The studies in [7], [8] reveal that the - fading is a suitable fading model for the line-of-sight multi-path propagation scenario. Moreover, the - fading model includes the classical fading models such as Nakagami- and Rice as special cases. Therefore, in this work we consider the generalized - fading.
The average symbol error rate (ASER) performance analysis of receivers employing QAM have been reported in literature for various fading environments in [3], [4], [9], [10], [11], [12], [13], [14], [15], [16], [17]. The authors in [9] obtained closed-form ASER expressions of several types of QAM schemes for a two-way multi-relay system in Nakagami- fading channels. The authors in [10], derived the ASER expression of RQAM for OFDM-based nonlinear AF relay network over Nakagami- fading channels. In [11], the authors derived ASER expressions of RQAM and XQAM for MRC and SC receiver in multiple AF relay network over Rayleigh fading channels. In [3], a closed-form expression for the exact ASER of RQAM scheme was derived for -branch selection combining (SC) receiver under independent and non-identically distributed (i.n.i.d.) Nakagami- fading. In [12], the authors obtained ASER expressions for RQAM scheme in multi-branch SC receiver under - fading considering integer values of . The authors in [13] derived an accurate approximation to ASER for RQAM scheme for -branch maximal ratio combining receiver in - and - fading scenarios. The authors in [14], derived analytical expressions for average bit error rate (ABER) and ergodic capacity performance for a SC receiver assuming double - fading. In [15], the ABER expressions for -branch SC receiver were derived for binary coherent and non-coherent modulation schemes assuming independent and identically distributed (i.i.d.) - and - fading channels. In [16], the ASER performance of RQAM schemes over composite fading channels was analyzed.
The ASER expression for HQAM assuming Rayleigh fading were derived in [4]. The ASER expressions of HQAM, RQAM and XQAM were derived for OFDM-based AF relay network over mixed Rician/Rayleigh fading channels in [17]. To the best of author’s knowledge, the ASER performance of SC receiver with RQAM and HQAM over i.n.i.d. - fading channels has not been studied in the literature. Motivated by the importance of RQAM and HQAM in emerging wireless technologies we study the performance of a SC receiver with RQAM and HQAM over - fading channels. In this paper, new exact expressions for moment generating function (MGF) of output signal-to-noise ratio (SNR), and ASERs of coherent RQAM, HQAM, and -ary non-coherent frequency shift keying (NCFSK) are presented. Further, asymptotic ASER expression is also obtained in the high SNR regime to examine the diversity order of the system.
The remainder of this paper is organized as follows: In Section 2, we describe the system and the channel model. The expressions for exact ASER and asymptotic ASER are derived in Section 3. Section 4 presents ASER results and discussions. The conclusions are presented in Section 5.
Section snippets
System and channel model
We consider a single-antenna transmitter and a multi-antenna receiver with antennas. We assume that the message symbol arriving at the branches is affected by multiplicative - fading and additive white Gaussian noise (AWGN). The receiver employs SC and the branch with the maximum instantaneous SNR is selected for decoding the message symbol at the receiver. Let denote the envelope of the - fading coefficient for the th branch, denote energy per symbol and denote the one sided
Error rate expressions
In this section, we derive exact expressions for ASER of coherent RQAM, HQAM, and NCFSK modulations. Moreover, asymptotic ASER expression is also obtained.
Numerical and simulation results
In this section, we present the ASER results for RQAM, HQAM and NCFSK schemes. For numerical analysis, we compute efficiently the function by its finite limit integral representation [21, (A10)]. Each infinite series in the ASER expression is truncated to terms such that the numerically evaluated ASERs match with the simulated ASERs. The minimum number of terms required for the numerical evaluation of ASER expression (10) is tabulated in Table 1 for a wide range of parameters. From
Conclusion
New exact expressions for MGF and ASER of RQAM, HQAM, and NCFSK modulations with -branch SC receiver over i.n.i.d. - fading channels have been derived. An asymptotic expression of ASER for RQAM has also been derived to obtain insights. The diversity order of -branch SC receiver over - fading channels is a function of and . The impact of , and on ASER has been investigated.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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