Abstract
This paper presents the mathematical model for symbol error probability of triangular quadrature amplitude modulation in a single-input multi-output environment. The symbol error probability performance is evaluated over fading channels namely Rayleigh, Nakagami-m, Nakagami-n, and Nakagami-q. The maximal-ratio combining technique is considered as spatial diversity algorithm and unified moment-generating-function-based approach is applied to derive the results. The multiple channels considered are independent but not necessarily identically distributed. The results presented are valid for slow and frequency non-selective fading channels only. The symbol error probability expressions obtained contain single integrals with finite limits and integrand composed of elementary functions which help us evaluate our analytical expressions numerically. We also compare these expressions with the error performances obtained through computer simulation, which show excellent agreement. In addition, an example has been simulated to validate our derived mathematical expressions.
Highlights
An efficient signal constellation has always been an active research area since 1960s for the purpose of wired and wireless communication
Though an exact generalized mathematical symbol error probability (SEP) expression in the presence of additive white Gaussian noise (AWGN) channel is provided in [11], the mathematical model we provide in this article can be implemented when dealing with triangular quadrature amplitude modulation (TQAM) in AWGN, and this model is extended to Rayleigh, Nakagami-m, Nakagami-n, and Nakagami-q channels
Since the four integrals from (44) to (55) are finite range, single integrals and integrand composed of elementary functions only; using (43), the average SEP of general modulation order TQAM with maximalratio combining (MRC) spatial diversity over fading channels can be conveniently assessed through numerical integration methods
Summary
An efficient signal constellation has always been an active research area since 1960s for the purpose of wired and wireless communication. SEP evaluation of TQAM over fading channels while using MRC diversity receiver demands knowledge of probability density function (pdf) of SNR γ∑ of the combined signal at output. We take a look at the pdf of the instantaneous received SNR per symbol γi of the ith diversity path over Rayleigh, Nakagami-m, Nakagami-n and Nakagami-q channels respectively, provided from [31] as: Fig. 3 SEP performance of M-TQAM in AWGN channel pγ i ;Rayleigh ðγ Þ. Ignoring the higher order terms Qi, i > 4, the average symbol error probability is approximately given as: Fig. 5 SEP performance of 64-TQAM in Rayleigh channel. Since the four integrals from (44) to (55) are finite range, single integrals and integrand composed of elementary functions only; using (43), the average SEP of general modulation order TQAM with MRC spatial diversity over fading channels can be conveniently assessed through numerical integration methods. The results illustrate the advantage of diversity as a means for combating the fading phenomena
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