# Performance of a L-branch predetection EGC receiver over independent Hoyt fading channels for M-ary coherent and noncoherent modulations using PDF-based approach

## Summary (2 min read)

### I. INTRODUCTION

- Performance of a predetection equal gain combining (EGC) diversity receiver in fading channels is known to be close to the performance of the optimum maximal ratio combining (MRC) receiver, with relatively less implementation complexity [1] .
- Recently, with an aim to generalize and obtain a better fit for the experimental data, several new fading distributions such as the κ-µ, η-κ and η-µ have been proposed [7] - [9] .
- Interestingly, in [7] an approximate but highly accurate PDF of the sum of independent Hoyt random variables (RVs) has been presented using moment based estimators.
- This useful result can be readily applied to analyze the performance of a L-branch predetection EGC receiver in independent Hoyt fading channels using PDF-based approach.
- In Section IV, the numerical evaluation steps have been discussed.

### II. CHANNEL AND RECEIVER

- The channel has been assumed to be slow, frequency nonselective, with Hoyt fading statistics.
- Assuming spatial diversity fading signals are available, a predetection EGC receiver with the structure as shown in Fig. 1 has been used for receiving the signals.
- The L-branch predetection EGC combiner cophases the received signals and produces at its output the algebraic sum of these cophased signals.
- The detector following the combiner is suitable for the detection of the signal, corresponding to the modulation scheme employed at the transmitter.
- The authors in a recent publication have presented this PDF which can be given as [10] EQUATION Using (5) it is now convenient to analyze different performance measures of a predetection EGC receiver in independent Hoyt fading channels using the PDF-based approach.

### C. Average Symbol Error Rate

- For a given modulation scheme, the ASER of any receiver can be obtained by averaging the conditional SER P(ε|γ) over the PDF of the receiver output SNR p γ (γ).
- For a number of M-ary modulation schemes these parameter values have been listed in Table I .
- The indefinite integral involved can be analytically solved using the identity [11, (3.381.4) ].
- The above expression (12) for the ASER of a predetection EGC receiver in Hoyt fading channels is useful for the following two major reasons:.
- Using the available software packages such as MATLAB and MATHEMATICA etc. this evaluation can be performed easily for a required degree of accuracy.

### 1) M-ary Phase Shift Keying Modulation: Substituting the parameters for MPSK modulation from Table I into (12), the ASER expression can be expressed as

- 2) M-ary Differential Phase Shift Keying Modulation: Substituting the parameters for MDPSK modulation from Table I into (12), the corresponding ASER expression can be given as EQUATION ) where f (θ) is defined in Table I .
- NUMERICAL EVALUATION Analytical expressions for P out (7) , AF (8) and ASER (13)-( 16) have been numerically evaluated.

### V. RESULTS AND DISCUSSION

- From the curves shown, it can be inferred that the severity of fading increases with increase in the fading parameter b and decreases with increase in L. ASER versus SNR E s /N 0 per branch has been plotted for MPSK and MDPSK modulations in Figs.
- It is important to observe the low SNR region of these plots where the curves are either crossing each other or overlapping.
- This gives an option to choose a less complex modulation scheme and/or less number of branches when receivers are likely to operate in low SNR environments.
- The plotted results have been compared with the matching cases in [5, Figs. 4(a) and 4(b)] and found to be matching closely.
- The observations from these plots can be explained in the manner similar to that presented for equal branch SNR case.

### VI. CONCLUSION

- The authors have analyzed the performance of a Lbranch predetection EGC diversity receiver in independent Hoyt fading channels, with non-identical and arbitrary fading parameters, applying the PDF based approach.
- Using an approximate but highly accurate expression for the PDF of the sum of independent Hoyt RVs, expressions for the outage probability, amount of fading and ASER have been obtained.
- The ASER expression is in the form of an infinite series with a single integral having finite limits and is applicable for a number of coherent and noncoherent modulation schemes.
- For the purpose of illustration, simplified expressions for the MPSK and MDPSK modulations have also been given.
- Numerically evaluated results have been plotted and compared with the particular cases of the published results to check the correctness of the obtained analytical expressions.

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27,354 citations

### "Performance of a L-branch predetect..." refers background in this paper

...where γ f ( ; ) is the incomplete gamma function [ 11 ]....

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### Additional excerpts

...,(14) where 2F1 (·, ·; ·; ·) is the Gaussian hypergeometric function [11]....

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...k!Γ ( μ+ k + (1)2 ) , (7) where γ f (·, ·) is the incomplete gamma function [11]....

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### "Performance of a L-branch predetect..." refers background or methods in this paper

...For unequal branch SNR case, an exponentially decaying power delay profile given by Ωl = Ω1e−δ(l−1),0 ≤ δ ≤ 1, has been assumed [1]....

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...Amount of Fading The AF is the measure of the severity of the fading channel often appropriate in the more general context of describing the behavior of diversity systems with arbitrary, combining techniques and channel statistics [1]....

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...This void eliminates the possibility of applying the direct and simple PDF-based approach [1] to the performance analysis of a predetection EGC receiver beyond L = 2....

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...Outage Probability The outage probability Pout is a standard performance criterion characteristic of diversity communication systems operating over fading channels [1]....

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...INTRODUCTION Performance of a predetection equal gain combining (EGC) diversity receiver in fading channels is known to be close to the performance of the optimum maximal ratio combining (MRC) receiver, with relatively less implementation complexity [1]....

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728 citations