M-ary Phase Shift Keying Modulation Research Articles

Performance of coherent FSO systems with adaptive M-PSK modulation

We investigate the performance of a heterodyne detection system with adaptive modulation that employs M-ary phase shift keying (M-PSK) modulation for transmission over a strong turbulence channel modeled by Gamma–Gamma distribution. The spectral efficiency (SE) and bit-error-rate (BER) expressions of the considered adaptive system are derived, where a new exact expression for the BER in terms of bivariate Fox’s H-function (BFHF) is presented. Furthermore, an asymptotic expression for the BER in terms of basic functions is introduced. The results show how much improvement in the SE that can be achieved when the adaptive system is used, where the modulation level is selected in accordance with the state of the channel, while maintaining the target BER. We also extend the adaptive system to a parallel-branches adaptive system employing the maximum ratio combining technique at the receiver, where the SE and BER are derived and analyzed to show the additional improvement in the SE when the number of branches is increased. Monte Carlo simulations are also provided to confirm the derived expressions.

Combined Radar and Communications With Phase-Modulated Frequency Permutations

This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using M-ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has a negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on a modified Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM. Extensive numerical examples are provided to illustrate the accuracy of our results.

Performance of MPSK modulation with imperfect phase‐recovery under severe fading conditions

The authors study the performance of M-ary phase-shift keying (MPSK) modulation with imperfect carrier phase recovery in scenarios experiencing severe fading conditions. Specifically, MPSK is analysed over κ $\kappa$ - μ $\mu$ Extreme fading channels assuming a Gaussian-distributed noisy phase. For the theoretical framework, they derive the analytical expressions for the upper bound on the average symbol error probability, as well as their corresponding asymptotic behaviour in the high signal-to-noise ratio (SNR) regime. The derived expressions are valid for arbitrary values of the fading parameter m $m$ , and Monte Carlo simulations are provided to verify the accuracy of the proposed mathematical analysis. Furthermore, the authors discuss how the channel parameter and phase variance affect the system performance for a wide range of SNR values.

Simulation of M-ary QAM and M-ary PSK Modulation Techniques Using MATLAB GUI

The world has seen a transformation due to the recent pandemic. The field of education is drastically affected by it. There is a need to move from classroom teaching to online teaching, and the biggest hurdle is to impart practical knowledge. This paper attempts to study the concepts like M-ary Phase shift keying (PSK) and M-ary Quadrature amplitude modulation (QAM), used in modern-day communication systems, using a simulation platform. For this purpose, simulation using a graphical user interface (GUI) is proposed to study various M-ary PSK and M-ary QAM types. MATLAB is used to implement the GUI. The modulation, transmission, demodulation, and recovery of a signal implemented through the GUI will help learners understand the concepts better. Moreover, the constellation diagrams for M-ary PSKs and M-ary QAMs can be examined using the developed GUI.

Error performance of digital modulations over Fisher-Snedecor F fading channels

In this paper, symbol error probability (SEP) and the average symbol error rate (ASER) of digital modulation schemes are derived in the presence of Fisher-Snedecor F fading. First, an analytical SEP expression is proposed based on complementary cumulative distribution function (CDF) for M-ary phase shift keying (M-PSK) and M-ary pulse amplitude modulation (M-PAM). Then, an asymptotic solution is also presented for the SEP of M-PSK and M-PAM modulations in order to get more insights on the performance at high signal-to-noise ratio (SNR) regime. Finally, an exact ASER expression for rectangular quadrature amplitude modulation (RQAM) is derived and then, the ASER performance is analyzed based on two different upper bound approximations of Gaussian Q-function in Fisher-Snedecor F fading channels. The proposed expressions are not only valid for integer values of fading and shadowing parameters but also valid for non-integer values. The performance results which are in good agreement with the exact simulations are illustrated for different modulation schemes and various configurations of fading and shadowing parameters.

Blind equalization and automatic modulation classification based on subspace for subcarrier MPSK optical communications

Equalization can compensate channel distortion caused by channel multipath effects, and effectively improve convergent of modulation constellation diagram in optical wireless system. In this paper, the subspace blind equalization algorithm is used to preprocess M-ary phase shift keying (MPSK) subcarrier modulation signal in receiver. Mountain clustering is adopted to get the clustering centers of MPSK modulation constellation diagram, and the modulation order is automatically identified through the k-nearest neighbor (KNN) classifier. The experiment has been done under four different weather conditions. Experimental results show that the convergent of constellation diagram is improved effectively after using the subspace blind equalization algorithm, which means that the accuracy of modulation recognition is increased. The correct recognition rate of 16PSK can be up to 85% in any kind of weather condition which is mentioned in paper. Meanwhile, the correct recognition rate is the highest in cloudy and the lowest in heavy rain condition.

Secure Space-Time Communications Over Rayleigh Flat Fading Channels

In this paper, we consider the wire-tap channel model consisting of three users, namely, a transmitter, a legal receiver, and an eavesdropper, where the eavesdropper has possible unlimited centralized or distributed multiple antennas, while the legal user has just a single antenna. With this model, we study the realization of strict positive secrecy rate through Rayleigh flat fading channels using M-ary phase shift keying (PSK) and orthogonal space-time block code (OSTBC) based on channel reciprocal principle. We demonstrate that the information rate at the eavesdropper can be reduced to zero and a positive communication rate at the legal receiver can be realized if the transmitter employs a proper phase precoder based on the channel reciprocal, and uses OSTBC and M-ary PSK modulations for data transmissions. Application examples of space-time codes for positive secrecy rate are illustrated. As we have given the eavesdropper more capabilities than the legal receiver and thus captured a worst case scenario, any positive secrecy rate that is achieved serves as a lower bound on the secrecy capacity.

Analysis of Amplify-and-Forward Cooperative Networks with Nakagami-m fading Channels For MRC Diversity Combining

In this paper we study the effect of diversity combining for Nakagami -m fading Channels in the amplify-and-forward cooperative networks.We derive the cumulative density function (CDF), probability density function (PDF) and moment generating function (MGF) for the multiple relay amplify-and-forward network with single half duplex channel maximal ratio combiner (MRC). In this network we investigate the cases of MRC at the destination, as well derive the exact Symbol Error Rate (SER) of M-ary phase-shift keying (M-PSK), and quadrature amplitude modulation (M-QAM) in Nakagami -m fading environment. We present a comparison between M-PSK and M-QAM modulation schemes in some representative scenarios where an arbitrary number of cooperative relays is considered.

Analysis of Amplify-and-Forward Cooperative Networks with Nakagami-m fading Channels For MRC Diversity Combining

In this paper we study the effect of diversity combining for Nakagami -m fading Channels in the amplify-and-forward cooperative networks.We derive the cumulative density function (CDF), probability density function (PDF) and moment generating function (MGF) for the multiple relay amplify-and-forward network with single half duplex channel maximal ratio combiner (MRC). In this network we investigate the cases of MRC at the destination, as well derive the exact Symbol Error Rate (SER) of M-ary phase-shift keying (M-PSK), and quadrature amplitude modulation (M-QAM) in Nakagami -m fading environment. We present a comparison between M-PSK and M-QAM modulation schemes in some representative scenarios where an arbitrary number of cooperative relays is considered.

BER of Subcarrier MPSK and MDPSK Systems in Atmospheric Turbulence

Bit-error rate (BER) performance of subcarrier $M$ -ary phase-shift keying (MPSK) and $M$ -ary differential PSK (MDPSK) is analyzed for optical wireless communications over Gamma–Gamma and lognormal turbulence channels. We study the relation between the exact BER and the approximate BER, which is obtained by dividing the symbol-error rate by the number of bits per symbol, for subcarrier MPSK and MDPSK modulations. The asymptotic BER performance gap between the exact and the approximate BERs is quantified analytically through our asymptotic analyses. The accuracy of the approximate BER of both MPSK and MDPSK depends on the channel conditions. Under weak turbulence conditions, the approximate BER expression can be used to predict the system performance with high accuracy, while under strong turbulence conditions the approximate BER becomes inaccurate and can only serve as a loose lower bound of the exact BER. The asymptotic BER performance loss of MDPSK with respect to MPSK is also quantified analytically.

Performance of M-QAM, M-DPSK and M-PSK with MRC diversity in a Nakagami-m fading channel

The nature of a wireless communication channel is very unpredictable. To design a good communication link, it is required to know the statistical model of the channel accurately. The average symbol error probability (ASER) was analyzed for different modulation schemes. A unified analytical framework was presented to obtain closed-form solutions for calculating the ASER of M-ary differential phase-shift keying (M-DPSK), coherent M-ary phase-shift keying (M-PSK), and quadrature amplitude modulation (QAM) over single or multiple Nakagami-m fading channels. Moreover, the ASER was estimated and evaluated by using the maximal ratio-combining (MRC) diversity technique. Simulation results show that an error rate of the fading channel typically depends on Nakagami parameters (m), space diversity (N), and symbol rate (M). A comparison between M-PSK, M-DPSK, and M-QAM modulation schemes was shown, and the results prove that M-ary QAM (M-QAM) demonstrates better performance compared to M-DPSK and M-PSK under all fading and non-fading conditions.

Impact of Uncertain Channel Estimation and Outdated Feedback on the Adaptive M-PSK Modulation

This paper investigates an adaptive M-ary phaseshiftkeying (M-PSK) modulation scheme over Rayleigh flatfading channels. The data rate is adapted according to thechannel state. At the receiver, the fading is estimated using pilot symbols. To cancel the channel impact, we correct the received signal by dividing it by the estimated value of the fading. So, we propose to adjust the modulation level by examining the statistics of the corrected signal. In contrast to the previous works on the adaptive M-PSK modulation techniques, our modulation switching protocol takes into account the channel estimation error variance. Moreover, we derive a new closed-form expression for the average bit error rate of the considered system.

Virtual Branch Analysis of Symbol Error Rate for OSTBC MIMO Systems with Generalized Selection Combining Using MPSK and MQAM Modulation Schemes

We consider a system where Generalized Selection Combining (GSC) is applied to a 4 x L Multiple-Input Multiple-Output (MIMO) system using Half rate-Full diversity Orthogonal Space-Time Block Codes (OSTBCs) at the transmitter. The Symbol Error Rate (SER) of M-ary Quadrature Amplitude Modulation (MQAM) for a slow, flat Rayleigh fading channel is derived and compared to that of the M-ary Phase Shift Keying (MPSK) modulation scheme. Performance comparisons of various antenna configurations are made. The channel statistics are assumed to be identical for the independent diversity branches. The effects of channel estimation errors on the SER performance for GSC are plotted and discussed in this paper. Index Terms—Multiple-input multiple-output (MIMO) systems, channel estimation error, generalized selection combining (GSC), space-time block codes (STBCs), quadrature amplitude modulation (QAM), symbol error rate (SER).

Performance Comparison of MIMO Systems over AWGN and Rician Channels with Zero Forcing Receivers

Multiple-Input Multiple-Output (MIMO) systems have been emerged as a technical breakthrough for high-data-rate wireless transmission. The performance of MIMO system can be improved by using different antenna selection so as to provide spatial diversity. In this paper, the performance of MIMO system over AWGN (Additive White Gaussian Noise) and Rician fading channels with ZF receiver is analyzed using different antenna configurations. The bit error rate performance characteristics of ZeroForcing (ZF) receiver is studied for M-PSK (M-ary Phase Shift Keying) modulation technique using AWGN and Rician channels for the analysis purpose and their effect on BER (Bit Error Rate) have been presented.

Cramér–Rao lower bound for non-data-aided carrier phase estimation from general M-ary phase-shift keying modulation signals over flat Rayleigh fading channel

The authors derive the true Cramér–Rao lower bound (CRLB) for a non-data-aided (NDA) carrier phase estimation from general M-ary phase-shift keying (M-PSK) modulation signal over flat Rayleigh fading channels (FRFC). The numerical Monte Carlo method is used to compute the true CRLB from general M-PSK modulation signals over FRFC with complex additive white Gaussian noise. The efficiency of the proposed method is made obvious through the assessment of the true CRLBs from both symmetric and asymmetric 8-PSK modulation signals for various observation window sizes. The simulation results show that optimal NDA carrier phase recovery is harder to acquire from symmetric modulation signals for signal-to-noise ratio (SNR) range up to 5 dB, but depends on the constellation density, only for SNR range superior to 5 dB. For both constellations the CRLB decreases as long as the observation window size increases. The derived bound provides an efficient standard for evaluating the performance of any unbiased NDA carrier phase estimator from general M-PSK modulation signals over FRFC. The method presented here stands useful for general M-ary quadrature amplitude modulation signals as well.

S+N Energy Selection Combining for MPSK and 16-QAM Signaling in Nakagami-m and Rician Fading Channels

A signal-plus-noise (S+N) energy selection diversity combining (S+N-ESC) scheme for M-ary phase shift keying (MPSK) in Rayleigh fading channels is mathematically analyzed. Also, the S+N-ESC scheme for MPSK and 16-quadrature amplitude modulation (16-QAM) signaling in Nakagami-m and Rician fading channels is studied by computer simulations. The S+N-ESC selects the branch with the maximum S+N energy for detection. The advantage of the S+N-ESC scheme is that it requires no explicit channel estimation for diversity branch selection. We show that the symbol error probability (SEP) of the S+N-ESC is the same as that of classical selection combining (SC) for MPSK signaling in independent and identically distributed (i.i.d.) Rayleigh fading channels. Also, we show that the SEP of a weighted S+N-ESC scheme is the same as that of classical SC for MPSK signaling in independent and nonidentically distributed (i.n.d.) Rayleigh fading channels. It is shown by computer simulations that the S+N-ESC scheme provides a smaller SEP than classical SC for MPSK signaling in nondispersive fading channels such as Nakagami-m fading channels with Nakagami parameter m >; 1 and Rician fading channels with Rician parameter K >; 0. On the other hand, the S+N-ESC scheme is shown by computer simulations to have a larger SEP than classical SC for 16-QAM signaling in Nakagami-m and Rician fading channels.

A symbol-by-symbol channel estimation receiver for space-time block coded systems and its performance analysis on the nonselective rayleigh fading channel

We present a symbol-by-symbol channel estimation receiver for an orthogonal space-time block coded system, and derive its analytical performance on a slow, nonselective, Rayleigh fading channel. Exact, closed-form expressions for its bit error probability (BEP) performance for M-ary phase shift-keying modulations are obtained, which enable us to theoretically predict the actual performance achievable under practical conditions with channel estimation error. Our BEP expressions show explicitly the dependence of BEP on the mean square error of the channel estimates, which in turn depend on the channel fading model and the channel estimator used. Tight upper bounds are presented that show more clearly the dependence of the BEP on various system parameters. Simulation results using various fading models are obtained to demonstrate the validity of the analysis.

Capacity Bound of MIMO Systems with MPSK Modulation and Time-Multiplexed Pilots

In this letter, we elucidate the ergodic capacity of multiple-input multiple-output (MIMO) systems with M-ary phase-shift keying (MPSK) modulation and time-multiplexed pilots in frequency-flat Rayleigh fading environment. With linear minimum mean square error (LMMSE) channel estimation, the optimal pilots design is presented. For mathematical tractability, we derive an easy-computing closed-form lower bound of the channel capacity. Based on the lower bound, the optimal power allocation between the data and pilots is also presented in closed-form, and the optimal training length is investigated by numerical optimization. It is shown that the transmit scheme with equal training and data power and optimized training length provides suboptimal performance, and the transmit scheme with optimized training length and training power is optimal. With the latter scheme, in most situations, the optimal training length equals the number of the transmit antennas and the corresponding optimal power allocation can be easily computed with the proposed formula.

Capacity Bound of MIMO Systems with MPSK Modulation and Superimposed Pilots

The enormous capacity potential of multiple-input multiple-output (MIMO) is based on some unrealistic assumptions, such as the complete channel state information (CCSI) at the receiver and Gaussian distributed data. In this paper, in frequency-flat Rayleigh fading environment, we investigate the ergodic capacity of MIMO systems with M-ary phase-shift keying (MPSK) modulation and superimposed pilots for channel estimation. With linear minimum mean square error (LMMSE) channel estimation, the optimal pilots design is presented. For the mathematical tractability, we also derive an easy-computing closed-form lower bound of the channel capacity. Furthermore, the optimal power allocation between the data and pilots is investigated by numerical optimization. It is shown that more power should be devoted to the data in low SNR environments and to the pilots in high SNR environments.

Error performance of optimum combining with MPSK modulation for dual-antenna diversity

New expressions are derived for the exact symbol error probability for the optimum combining of M-ary phase shift keying (MPSK) signals over dual-antenna diversity reception. A flat Rayleigh fading environment with multiple equipower cochannel interferers and additive white Gaussian noise is considered. The derived expressions facilitate the numerical computation as they only depend on well-known mathematical functions. Also, a simple tight approximation is proposed. Copyright © 2005 AEIT.