Noncoherent M-ary Frequency Shift Keying Research Articles

Dual-hop communications over PLC/η-μ and PLC/λ-μ fading channels

ABSTRACT In this study, the performance analysis of dual-hop power line communication (PLC)/ and PLC/ L-branch systems by using the decode-and-forward (DF) protocol is presented in detail. The introduced work provides novel closed-form expressions of the probability density function (PDF) of the instantaneous signal-to-noise ratio (SNR) of the considered systems. Taking the proposed PDFs into account, we also derive closed-form expressions of the error rate and channel capacity (CC) performance for the dual-hop PLC/ and PLC/ L-branch DF systems. Furthermore, an exhaustive comparative study of different modulation types such as non-coherent M-ary frequency-shift keying, square quadrature amplitude modulation (SQAM), and cross quadrature amplitude modulation (×QAM) is presented by using the proposed closed-form error rate expressions. Also, the exact expressions for the CC with channel inversion with a fixed-rate (CIFR) transmission policy are proposed. Finally, all the theoretical findings are confirmed through numerical results obtained by using the exact expressions.

PERFORMANCE ANALYSIS OF ASYNCHRONOUS FFH-MA UNDER THE PRESENCE OF THE FREQUENCY OFFSET

In order to investigate the effect of asynchronous fast frequency hopping-multiple access (FFH-MA) systems due to the frequency offset, we evaluate the bit error rate (BER) performance, using noncoherent Mary frequency shift keying (FSK) modulation in the Rayleigh fading channel. While the frequency offset increases at a given signal to noise ratio (SNR), the BER is severely degraded due to the loss of orthogonality of received symbols. With 10% frequency offset, about 5 dB SNR is required additionally to obtain 2 x 10-3 BER, compared to that in the perfectly frequency synchronized case. For the SNR of more than 20 dB, the threshold level of the receiver suffering from the frequency offsets should be greater than that of the perfectly synchronized receiver.

Energy Harvesting Noncoherent Cooperative Communications

This paper investigates simultaneous wireless information and power transfer (SWIPT) in energy harvesting (EH) relay systems. Unlike the existing SWIPT schemes requiring the instantaneous channel state information (CSI) for coherent information delivery, we propose a noncoherent SWIPT framework for decode-and-forward (DF) relay systems bypassing the need for the instantaneous CSI and consequently saving energy in the network. The proposed SWIPT framework embraces both the power-splitting noncoherent DF (PS-NcDF) and timeswitching noncoherent DF (TS-NcDF) in a unified form, and supports arbitrary M-ary noncoherent frequency-shift keying (FSK) and differential phase-shift keying (DPSK). The exact (noncoherent) maximum-likelihood detectors (MLDs) for PS-NcDF and TS-NcDF are derived in a unified form, which involves integral evaluations yet serves as the optimum performance benchmark for noncoherent SWIPT. To reduce the computational cost of the exact MLDs, we also propose closed-form approximate MLDs achieving near-optimum performance, thus serving as a practical solution for noncoherent SWIPT. Numerical results demonstrate a performance tradeoff between the first and second hops through the adjustment of time switching or power splitting parameters, whose optimal values minimizing the symbol-error rate (SER) are strictly between 0 and 1. We demonstrate that M-FSK results in a significant energy saving over M-DPSK for M ≥ 8; thus M-FSK may be more suitable for EH relay systems.

Approximation to independent lognormal sum with α–μ distribution and the application

This paper considers the statistical distribution of the sum of independent and possibly non-identically distributed lognormal random variables (RVs). The α–μ distribution is employed to approximate the probability of density function (PDF) of the lognormal sum. Two approaches, e.g., the moment-based and non-linear least square based (LS-based) methods, are used to obtain the parameters of α–μ distribution. Accounting for maximal-ratio combining (MRC) receiver, an analytical expression of the average bit error probability (ABEP) of the M-ary noncoherent frequency-shift keying (M-NFSK) modulation is derived. Finally, the performances of the α–μ approximation and the ABEP are evaluated via numerical experiments.

Performance of M-ary turbo coded synchronous FHSS multiple access networks with noncoherent MFSK under Rayleigh fading channels

The performance of M-ary turbo coded synchronous, fast frequency-hopping spread spectrum multiple-access (FHSS-MA) networks with M-ary frequency shift keying (MFSK) and noncoherent detection is analyzed under Rayleigh fading. Results indicate that M-ary turbo codes dramatically enhance the performance of FHSS-MA networks using MFSK compared to binary turbo codes.

SNR Estimation for Non-Coherent M-FSK Receivers in Rice Fading Environment

The problem of estimating the average signal-to-noise ratio (SNR) in a non-coherent M-ary frequency shift keying (NCMFSK) receiver has been considered, where the transmitted signal is propagated over a noisy Ricean fading channel. Closed-form maximum likelihood estimators for both the data-aided and non data-aided scenarios have been derived using the approximations of the modified Bessel functions. Numerical results are presented and the performance of the estimators is evaluated by comparing with a Cramer-Rao bound.

Noncoherent Amplify-and-Forward Cooperative Networks: Robust Detection and Performance Analysis

We develop closed-form generalized likelihood ratio test (GLRT) sequence detectors for multi-relay amplify-and-forward (AF) cooperative networks employing M-ary differential phase-shift keying (M-DPSK) and noncoherent M-ary frequency-shift keying (M-FSK). The proposed detectors achieve robust performance in a wide range of fading environments where prior knowledge of channels, signal powers, noise variances, and relay functionalities is unavailable to the destination. A comprehensive error probability performance analysis is carried out in Rayleigh fading. Specifically, we derive unified pairwise error probability (PEP) expressions for both detectors in a dual-hop network, which are valid for arbitrary modulation order M and arbitrary sequence length N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> . We also derive unified bit-error probability (BEP) expressions for both detectors employing binary signalings in various networks for N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = 1. It is further shown that both detectors achieve near full diversity orders. Finally, the superiorities of the proposed detectors over the state-of-the-art noncoherent detectors are justified through extensive comparisons in practical scenarios. For example, in a multi-relay network where the relays are uniformly distributed between the source and destination, the proposed detector for noncoherent FSK with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = 1 outperforms the well-known maximum energy selector by almost 15 dB in high signal-to-noise ratios.

SNR Estimation for M-ARY Non-Coherent Frequency Shift Keying Systems

This paper considers how to estimate the average signal-to-noise ratio (SNR) for a communication system employing orthogonal non-coherent M-ARY frequency shift keying (NCMFSK), in white Gaussian noise (AWGN) and over both symbol-by-symbol fading channels and block fading channels. The proposed algorithm finds its application in a variety of applications including a cooperative transmission system, which is the main motivation behind this study. The maximum likelihood estimator and one using data statistics have been derived and simulated for various scenarios including data-aided, non-data aided and joint estimation using both the data and pilot sequences. We also derive the Cramer-Rao bound for the estimators in the case of Rayleigh fading channels. The results show that for a particular region of interest (e.g. high SNR or low SNR) and depending upon the availability of pilot sequence, a particular SNR estimation scheme is suitable.

Soft Metrics and EXIT Chart Analysis of Noncoherent MFSK with Diversity Reception in Rician Fading Channel

A convolutionally encoded noncoherent M-ary Frequency Shift Keying (MFSK) modulation scheme with diversity reception is considered. Soft metrics for Soft Decision Decoding (SDD) of noncoherent MFSK are derived assuming Rician channel model. Furthermore, the convergence behavior of the MFSK receiver is investigated using EXtrinsic Information Transfer (EXIT) charts. It has been demonstrated that the derived expressions for soft information are useful allowing SDD of the MFSK scheme exploiting diversity and the EXIT chart analysis provides useful insights into its iterative decoding behavior.

Green modulations in energy-constrained wireless sensor networks

Owing to the unique characteristics of sensor devices, finding the energy-efficient modulation with a low-complexity implementation (refereed to as green modulation) poses significant challenges in the physical layer design of wireless sensor networks (WSNs). Towards this goal, the authors present an in-depth analysis on the energy efficiency of various modulation schemes using realistic models in the IEEE 802.15.4 standard to find the optimum distance-based scheme in a WSN over Rayleigh and Rician fading channels with path loss. The authors describe a proactive system model according to a flexible duty-cycling mechanism utilised in practical sensor apparatus. The present analysis includes the effect of the channel bandwidth and the active mode duration on the energy consumption of popular modulation designs. Path-loss exponent and DC–DC converter efficiency are also taken into consideration. In considering the energy efficiency and complexity, it is demonstrated that among various sinusoidal carrier-based modulations, the optimised non-coherent M-ary frequency shift keying (NC-MFSK) is the most energy-efficient scheme in sparse WSNs for each value of the path-loss exponent, where the optimisation is performed over the modulation parameters. In addition, the authors show that the on–off keying displays a significant energy saving as compared to the optimised NC-MFSK in dense WSNs with small values of path-loss exponent.

Jamming 환경에서 SFH 변조 방식에 따른 위성 통신 시스템의 BER 성능 분석

FHSS(Frequency Hopping Spread Spectrum) 방식은 군 통신 시스템에서 재밍(Jamming)에 의한 간섭을 줄이기 위해 사용된다. 하지만 사용되는 변조 방식의 종류, 재밍 신호의 특성에 따른 위성 통신 시스템의 BER 성능이 무선 채널 상태에 따라 어떤 성능 차이를 보이는지 분석되지 않았다. 따라서 본 논문에서는 PBNJ(Partial-Band Noise Jamming)와 WPBJ(Worst case Partial-Band noise Jamming)의 두 가지 재밍 환경에서 NC-MFSK(Non-Coherent M-ary Frequeency-Shift Keying), SDPSK(Symmetric Differential Phase-Shift Keying), GMSK (Gaussian filtered Minimum-Shift Keying)의 세 가지 변조 방식에 따른 위성 통신 시스템의 BER 성능 변화를 분석한다. 또한, 분석된 결과를 이용하여 전송 환경에 따른 최적의 전송 방식을 제안하도록 한다. The FHSS(Frequency Hopping Spread Spectrum), in which a transmitter changes its carrier frequency according to a certain hopping pattern, is widely used in the military communication system, since it is highly resistant to deliberate Jamming. However, the difference of BER performance of satellite communication system which using the different modulation scheme and Jamming model was not studied. Thus, in this paper, we consider PBNJ(Partial-Band Noise Jamming) and WPBJ(Worst case Partial-Band noise Jamming) as Jamming models, and evaluate BER(Bit Error Rate) performances of NC-MFSK(Non-Coherent M-ary Frequency-Shift Keying), SDPSK(Symmetric Differential Phase-Shift Keying), and GMSK(Gaussian filtered Minimum-Shift Keying) modulation schemes. Based on the results, we suggest the best transmission method for each condition.

A Unified Framework for Interference Analysis of Noncoherent MFSK Wireless Communications

This paper presents a new unified analytical technique for accurate interference analysis of noncoherent M-ary frequency shift keying (MFSK) wireless communication systems in the presence of additive white Gaussian noise (AWGN) and multiple arbitrary interfering signals. New exact bit error rate expressions are derived for nonorthogonal noncoherent binary FSK in the presence of an arbitrary number of interfering signals having arbitrary spectral shapes at arbitrary frequency offsets. Furthermore, tight upper bounds for the symbol and bit error rates are given for noncoherent MFSK with arbitrary tone spacings. These results are extended to include MFSK signals experiencing Rayleigh, Nakagami-m or Rician fading. Some specific interference scenarios are analyzed in details, including jammers with a given Doppler-spread, direct sequence spread spectrum and orthogonal frequency division multiplexing signals, and a Poisson field of arbitrary interferers.

A performance comparison of erasure tests with diversity reception for noncoherent M-ary FSK signaling [Transactions Papers

A l-Bayesian erasure test (BET) based on order statistics with diversity reception for noncoherent M-ary frequency shift keying (FSK) signaling is examined. In the l-BET, the M-ary FSK symbol is erased whenever the a posteriori probability of correct decision, which is a function of the l-largest sums of energy detector outputs, is less than a threshold. For binary FSK signaling in Rayleigh flat fading channels, the 2-BET is found to be the same as the difference threshold test (DTT), which declares an erasure whenever the difference between the largest and the second largest sums of energy detector outputs is less than a threshold. The output threshold test (OTT), which declares an erasure whenever the largest sum of energy detector outputs is less than a threshold, is proved equivalent to the 1-BET for the Rayleigh flat fading channel. Closed-form expressions for the probabilities of correct decision and symbol error for the DTT, Viterbi's ratio threshold test (RTT), and the OTT are derived when square-law combining (SLC) diversity is used. Several erasure tests including the Z-BET, the RTT, the OTT, and the DTT are compared in terms of probability of codeword error. The 2-BET provides almost the same performance as the BET that requires all the sums of energy detector outputs. The 2-BET provides power gains of 0.9 dB and 0.7 dB over the RTT for (7, 3) and (15, 7) Reed-Solomon (RS) codes, respectively, when the probability of codeword error is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and the diversity order is one.

Average BER Analysis for $M$-ary FSK Signals in Nakagami-$q$ (Hoyt) Fading With Noncoherent Diversity Combining

This paper analyzes the average bit error rate (BER) of noncoherent M-ary frequency-shift keying (FSK) signals over multichannel nonidentically distributed Nakagami-q (Hoyt) fading employing diversity combining. The first part of the paper considers the conventional postdetection noncoherent equal-gain combiner (NC-EGC), in which a Fourier series inversion formula is employed to derive a simple and rapidly converging series-based expression for the system average BER. This expression is valid for arbitrary values of received average signal-to-noise ratios (SNRs) and fading parameters. The derived expression is then compared with some existing ones in the literature, and the results show a large reduction in computational complexity, particularly when M and/or the diversity order increases. In the second part, a new noncoherent combiner is proposed to achieve improvements over the conventional NC-EGC. It is also shown that this new combiner results in a simple closed-form expression for the system average BER that is given in terms of elementary functions; hence, it can be easily numerically evaluated with noticeable computation efficiency.

Performance of S + N Selection Diversity Receivers in Correlated Rician and Rayleigh Fading

The performances of two signal-plus-noise (S + N) selection diversity receivers employing noncoherent M-ary frequency shift keying (MFSK) in slow, flat, correlated Rayleigh and Rician fading channels are examined. The branches are assumed to be equally correlated for Rician fading. The correlation model for Rayleigh fading is more general than the equally correlated scenario and includes it as a special case. Analytical expressions are derived for the average symbol error rate (SER) and the average bit error rate (BER) of each receiver structure. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The performances of the S + N SC receivers are compared to the performance of the classical SC receiver. The effects of correlation, average fading power imbalance and diversity order on the performances of the S + N SC receivers are examined.

Performance of Two Dual-Branch Postdetection Switch-and-Stay Combining Schemes in Correlated Rayleigh and Rician Fading

The performance of binary frequency-shift keying (BFSK) and M-ary frequency shift keying (MFSK) with dual-branch postdetection switch-and-stay combining (SSC) in correlated Rayleigh and Rician fading is studied. Two postdetection SSC receivers are considered and the performances of noncoherent BFSK and MFSK are analyzed. Closed-form expressions are derived for the average bit-error rate (BER) of BFSK and MFSK with postdetection SSC in correlated Rayleigh and Rician fading. Optimum switching thresholds that minimize the average BER are obtained. Extensive Monte Carlo simulations are presented to test the validity of the analytical results. The performance of dual-branch postdetection SSC is compared with the performance of dual-branch predetection SSC. The effects of correlation, fading parameter, average fading power imbalance, and switching threshold on the performances of postdetection SSC receivers are examined

Simple SER formulas for noncoherent MFSK with square-law diversity combining in generic nakagami-m fading

The error performance of M-ary frequency shift keying (MFSK) with square-law diversity combining (SLDC) on correlated Nakagami-m fading channels was previously analyzed in the literature. The results are either in the form of an integral, or a closed form involving the calculation of higher-order derivatives, or other closed forms subject to the constraint of integer-valued fading parameters. In this letter, we formulate the problem in the framework of Lauricellar hypergeometric functions leading to a simple symbol-error-rate formula involving only some elementary functions for generic correlated Nakagami fading environments

SER of M-ary NCFSK with S + N Selection Combining in Nakagami Fading for Integer m

The performance of M-ary orthogonal noncoherent frequency-shift keying (NCFSK) with N branch signal-plus-noise (S + N) selection combining (SC) in Nakagami-m fading (m, integer) is studied. Both independent, identically distributed (i.i.d) and independent, nonidentically distributed (i.n.d) diversity branches are considered and two S + N SC receiver structures are examined. The performances of the S + N SC receivers are compared to those of classical SC and square-law combining (SLC) receivers. The effects of modulation order, fading parameter and the number of diversity branches on the performance of S + N SC are compared to the effects on the performances of classical SC and SLC. For example, it is shown that in an i.n.d fading channel, the value of signal-to-noise ratio (SNR) at which the error rate curves of classical SC and S + N SC cross, decreases as the modulation order, M, increases. Our results indicate that in i.n.d fading channels classical SC outperforms S + N SC for small ranges of SNR, while for moderate to large SNR values S + N SC has superior performance over classical SC. It is also shown that increasing the diversity order will increase the performance gap of S 4N SC over classical SC and over SLC in both i.i.d and i.n.d Nakagami-m fading channels

Analysis of asynchronous FFH-MA systems with a hard-limited combining in Rayleigh fading

The bit error rate (BER) performance of the asynchronous fast frequency hopping multiple access (AFFH-MA) system with multiple hops per symbol is investigated considering the noncoherent M-ary frequency shift keying (MFSK) modulation and hard-limited linear combiner in Rayleigh fading. We present a method for the accurate evaluation of the BER of the AFFH-MA system, and verify the analytic works by Monte Carlo simulations.

On the Optimality of Bit Detection of Certain Digital Modulations

In this paper, we study the optimality of bit detection for coherent M-ary phase-shift keying (PSK) and M-ary quadrature amplitude modulation (QAM), and noncoherent M-ary frequency-shift keying (FSK) signal sets. For M-PSK and M-QAM signal constellations, we employ Gray mapping, consider 8-PSK and 16-QAM signal sets as representative of the general results, and derive the log-likelihood ratio (LLR) for each bit forming the symbol. Using the LLRs, we derive the average bit-error probability (BEP) for the individual bits, and show that the decision regions and the corresponding average BEP for the case of M-PSK coincide with those obtained with the optimal symbol-based detector, whereas, in general, this is not the case for both M-QAM and M-FSK.