Exact Symbol Error Rate Research Articles

On the Error Performance of LoRa-Enabled Aerial Networks Over Shadowed Rician Fading Channels

UAVs can be used as aerial relays to provide communication services in remote uncovered areas or dense environments with occasional high capacity demands. However, due to the low power of Internet-of-Things (IoT) devices, UAV-based IoT applications, such as precision agriculture and environment monitoring, may experience high shadowing or equipment failure, which degrades the communications’ quality between IoT devices and their gateways. To tackle this issue, we consider the long range (LoRa) communication technology. Specifically, we investigate the performance of LoRA-enabled aerial communications, where a LoRa gateway communicates with a distant IoT device through the assistance of an amplify-and-forward (AF) aerial relay. Under the assumption of shadowed Rician fading channels, we characterize at first the end-to-end LoRa communication link. Then, we derive an exact symbol error rate expression for the underlying system model. Finally, numerical results are presented to corroborate the efficacy of our derived expressions and provide valuable insights into the error performance of LoRa-enabled aerial networks.

CSIN-assisted AF dual-hop relaying communication systems over imperfect Nagakami-[formula omitted] fading channels: Exact error performance

Relaying-based communication techniques are promising for current and future wireless systems. Amplify-and-forward (AF) relaying is more attractive due to the low cost and simplicity in its relay implementation. As compared to other AF schemes, the channel-state-information (CSI)-and-noise (CSIN)-assisted one is optimal and practically recommended. However, up to this moment, the exact symbol error rate (SER) performance of CSIN-assisted AF dual-hop relaying systems has been analytically derived only for Rayleigh fading environments, while for other more generic fading models, including Nakagami-m, it has been computed either approximately or via long-running time computer simulations. Thus, in this paper, we consider a CSIN-assisted AF dual-hop relaying system with independent and non-identical Nakagami-m fading channels and derive a new expression for its exact SER performance under the effect of imperfect channel estimation. The derived expression includes infinite series that can truncate quickly using a few terms, requires short computational time as compare to simulation, shows perfect matching with the simulation results, and offers remarkable accuracy enhancement over its approximate peer derived in literature. In addition, it helps in demonstrating some useful insights into the system’s realistic error performance considering different system and fading severity conditions. For example, results show that the system’s exact SER performance is dominated by the worse fading hop, does not change when the system’s two fading hops exchange their fading conditions, and improves faster with the per symbol average SNR when the fading severity conditions are better.

Exact SER and BER Analysis on Jointly Optimal Maximum Likelihood Detection of Two QPSK Signals With Phase Offset

Analysis on the exact error rate of jointly optimal (JO) maximum likelihood (ML) multiuser detection is limited in the existing literature owing to its high computational complexity. In this paper, the JO ML detection of two quadrature phase-shift keying (QPSK) signals with an arbitrary relative phase offset is investigated. Exact, analytical symbol error rate (SER) and bit error rate (BER) formulas are derived for two users with no less than 3 dB power difference between them. Closed-form union bounds on the user SER and BER with an arbitrary phase offset and an arbitrary user power ratio are also given as a simpler approach to acquire the asymptotic error rate performance. Furthermore, insights on the potentials and properties of the JO ML detector regarding its error rate behaviors for each user are revealed through comparisons with the successive interference cancellation receiver. The accuracies of the obtained formulas are demonstrated through simulation. The results show the error rates for the two-user QPSK case no longer follow the classic knowledge on the error rate behaviors in the single signal detection. In addition, the performance and dB penalty employing different modulation types are also compared and discussed.

Intelligent Reflecting Surfaces Assisted UAV Communications for IoT Networks: Performance Analysis

The increasing demand for wireless connectivity and the emergence of the notion of the Internet of Everything require new communication paradigms that will ultimately enable a plethora of new applications and new disruptive technologies. In this context, the present contribution investigates the use of the recently introduced intelligent reflecting surface (IRS) concept in unmanned aerial vehicles (UAV) enabled communications aiming to extend the network coverage and improve the communication reliability as well as spectral efficiency of Internet of Things (IoT) networks. In particular, we first derive tractable analytic expressions for the achievable symbol error rate (SER), ergodic capacity, and outage probability of the considered set up. Following this, we also derive tight upper and lower bounds on the average signal-to-noise ratio (SNR). Our derivations are then compared with the corresponding asymptotic performance, based on the central limit theorem (CLT) assumption, which reveals that the asymptotic SNR falls within the area between derived bounds, and approaches either bound depending on the number of reflective elements (REs). We further show that the asymptotic SER becomes in a tight agreement with the corresponding exact simulation SER for N ≥ 16. In addition, the offered results demonstrate that the use of the IRS is significantly effective as they assist in improving the achievable SER by five orders of magnitude. We further demonstrate that, in terms of achievable ergodic capacity, IRS-assisted UAV communication systems can exhibit ten times higher capacity compared to conventional UAV communications. Based on the above, these results and related insights are anticipated to be useful in the design and deployment of IRS-assisted UAV systems in the context of beyond 5G communications, such as 6G communications.

Symbol error rate analysis of non-orthogonal multiple access systems

Non-orthogonal multiple access (NOMA) systems use superposition coding (SC) at transmitter and successive interference cancellation (SIC) at the receiver in order to simultaneously transmit the messages of multiple users. In this paper, closed from expressions for the symbol error rate (SER) of superposition codes are derived. Moreover, an approximate expression is presented and it is shown that it closely follows the exact symbol error rate. The derived formulas are applicable to general scenarios with N users when each individual user uses pulse amplitude modulation (PAM) or quadrature amplitude modulation (QAM) signalling with arbitrary constellation sizes. While the error expressions are for additive white Gaussian noise (AWGN) channels, it will be shown that they can be extended to fading channels. Numerical simulations verify the validity of both expressions.

Phase-Jitter based SER of MPSK Scheme over Generalised Mixture Gamma Fading

ABSTRACTExtensive literature exists for simple and exact expressions of symbol error rate (SER) over fading channels under different modulation schemes whose boundaries meet at right angles. In cases where boundaries do not meet at right angles, integrals of special function in the expressions make the exact calculation most complex. In such cases only approximate solutions are possible. Also, it is noteworthy to mention that when detection is performed with proper use of the phase (phase-jitter-based approach), noise performance of the receiver improves significantly. This paper applies phase-jitter PDF-based approach to present exact and closed-form SER expression of MPSK scheme over Mixture Gamma (MG) distribution for an arbitrary array of signal points. The proposed expression is generic as MG distribution can be approximated in almost all fading/shadowed fading channel models. As a proof to the authenticity, SERs of MPSK scheme over Rayleigh and Nakagami-m fading channels are deduced from the proposed SER over generalised MG distribution. Further, a significant improvement in SER has been achieved with phase-jitter-based approach as compared to conventional (non-phase-jitter-based) approach. Finally, to confirm the correctness of the proposed expression, results are validated through comparison with the existing results and Monte Carlo simulation.

Symbol Error Rate Analysis of OFDM System with CFO Over TWDP Fading Channel

In this manuscript, an exact symbol error rate analysis of orthogonal frequency division multiplexing system is presented in the presence of carrier frequency offset over two wave with diffuse power (TWDP) fading channel. Both Binary Phase Shift Keying and Quadrature Phase Shift Keying modulation techniques are considered in this study over TWDP channel which contains Rayleigh, Rician and two ray fading as its special cases. The results are validated by means of Monte Carlo simulations and also verified from the benchmark results available in the literature.

Closed-Form Symbol Error Rate Expressions for Non-Orthogonal Multiple Access Systems

In this paper, the reliability performance of a non-orthogonal multiple access (NOMA) system is addressed. We characterize the reliability performance of the users in a downlink power domain NOMA system with arbitrary ordered pulse-amplitude modulation and quadrature amplitude modulation. In particular, the exact symbol error rate (SER) expressions are derived. Furthermore, by taking the power allocation between users into account, a reliability optimization problem is formulated, which minimizes the SER of the user with a good channel quality while guaranteeing the reliability requirement for the user with a relatively poor channel. Based on the characterized SER model, a suboptimal power allocation approach for this problem is provided with a performance extremely close to the optimal solution. Through simulations, we validate the provided SER characterization and confirm the effectiveness of the proposed suboptimal power allocation policy.

Exact error rate analysis of two-hop AF Rayleigh fading cooperative systems with variable amplification gain

A careful exploration of literature confirms that exact symbol-error-rate (SER) performance of amplify-and-forward (AF) wireless cooperative communication systems with variable amplification gain has not been analyzed before; even for simple models with single relay (i.e, two-hop systems) and Rayleigh fading channels. The main source of this mathematical intractability is the appearance of the modified Bessel function of the second type Kν(·) in the statistics of these systems end-to-end SNR. Here, however, we aim at filling this literature gap by proposing a novel theoretical method that helps in examining, for the first time, the exact SER performance of two-hop AF systems, where, as a case study, we assume Rayleigh quasi-static fading environment with perfect channel estimation. Specifically, we derive two new exact expressions for the system’s SER performance, which involve rapidly convergent infinite summation(s) and efficiently computable special functions. Furthermore, for the same system, we obtain new approximate closed-form SER expression, which outperforms its literature counterpart. The obtained analytical results are useful to gain insight about the actual error performance of variable gain AF systems. The presented methodologies can form a generic framework for exact SER performance evaluation of other variable gain AF cooperative system models.

Performance Analysis of Semi-Coherent OFDM Systems With Imperfect Channel Estimates

This work presents the exact symbol error rate (SER) analysis of semi-coherent demodulated systems in the presence of imperfect knowledge of the channel estimates. The SER is derived in the context of orthogonal frequency division multiplexing (OFDM) systems where a modulation-hybrid frame structure is considered to enable blind channel estimation using a decision-directed approach. The exact SER is derived and presented in a closed-form analytical expression, which is then used to compute an accurate formula for the mean squared error (MSE) of the channel estimates. The obtained analytical and simulation results show that the SER and MSE are highly dependent on the channel correlation factor. However, reliable SER can still be obtained for most practical channel models, particularly when receiver diversity is incorporated.

Cognitive Heterogeneous Networks with Unreliable Backhaul Connections

To enhance the spectrum scarcity of cooperative heterogeneous networks (HetNets) with unreliable backhaul connections, we examine the impact of cognitive spectrum sharing over multiple small-cell transmitters in Nakagami-m fading channels. In this system, the secondary transmitters are connected to macro-cell via wireless backhaul links and communicate with the secondary receiver by sharing the same spectrum with the primary user. Integrating cognitive radio (CR) network into the system, we address the combined power constraints: 1) the peak interference power at the primary user and 2) the maximal transmit power at the secondary transmitters. In addition, to exclude the signaling overhead for exchanging channel-state-information (CSI) at the transmitters, the selection combining (SC) protocol is assumed to employ at the receivers. To evaluate the performance, we first derive the closed-form statistics of the end-to-end signal-to-noise (SNR) ratio, from which the exact outage probability, ergodic capacity and symbol error rate expressions are derived. To reveal further insights into the effective unreliable backhaul links and the diversity of fading parameters, the asymptotic expressions are also attained. The two interesting non-cooperative and Rayleigh fading scenarios are also investigated. Numerical results are conducted to verify the performance of the considered system via Monte-Carlo simulations.

Resource Allocation for Multicarrier Device-to-Device Video Transmission: Symbol Error Rate Analysis and Algorithm Design

In resource allocation for a device-to-device (D2D) video transmission system, the performance improvement by applying the exact symbol error rate (SER) is compared with the conventional signal-to-interference-plus-noise-ratio-based SER evaluation method that uses a Gaussian approximation (GA) for the aggregated interference. An analytical SER expression for a D2D system using multicarrier bandlimited QAM is derived and then used in the resource allocation algorithm. We consider centralized resource allocation for the D2D system, given knowledge of the channel state information and the rate distortion information of the video streams, and propose an iterative algorithm for subcarrier assignment and power allocation. Bit-level simulations for different numbers of D2D pairs demonstrate a considerable improvement on user capacity and video peak signal-to-noise ratio by incorporating the proposed SER expression compared with the GA. By invoking the conditions under which the central limit theorem holds, and comparing these conditions with the number of interferers and the power ratio of the dominant interferer in the simulated D2D system, we also study why the GA for the interference degrades performance.

Performance Characterization of a Hybrid Satellite-Terrestrial System with Co-Channel Interference over Generalized Fading Channels.

The transmission of signals in a hybrid satellite-terrestrial system (HSTS) in the presence of co-channel interference (CCI) is considered in this study. Specifically, we examine the problem of amplify-and-forward (AF)-based relaying in a hybrid satellite-terrestrial link, where the relay node is operating in the presence of a dominant co-channel interferer. It is assumed that direct connection between a source node (satellite) and a destination node (terrestrial receiver) is not available due to masking by obstacles in the surrounding. The destination node is only able to receive signals from the satellite with the help of a relay node located at the ground. In the proposed HSTS, the satellite-relay channel follows the shadowed Rice fading; and the channels of interferer-relay and relay-destination links experience generalized Nakagami-m fading. For the considered AF-based HSTS, we first develop the analytical expression for the moment generating function (MGF) of the overall output signal-to-interference-plus-noise ratio (SINR). Then, based on the derived exact MGF, we derive novel expressions for the average symbol error rate (SER) of the considered HSTS for the following digital modulation techniques: M-ary phase shift keying (M-PSK), M-ary quadrature amplitude modulation (M-QAM) and M-ary pulse amplitude modulation (M-PAM). To significantly reduce the computational complexity for utility in system-level simulations, simple analytical approximation for the exact SER in the high signal-to-noise ratio (SNR) regime is presented to provide key insights. Finally, numerical results and the corresponding analysis are presented to demonstrate the effectiveness of the developed performance evaluation framework and to view the impact of CCI on the considered HSTS under varying channel conditions and with different modulation schemes.

Concise SER Analysis of Differential Quaternary Phase Shift Keying with Gray Coding Over Composite Multipath Shadowing Channels

To effectively assess the symbol error rate (SER) performance achieved by π/4 differential quaternary phase shift keying (π/4-DQPSK) with Gray coding over Rician-Nakagami fading channels, a simple closed-form asymptotic SER formula is derived, which is much simpler than the existing exact SER expression. From the proposed simple closed-form formula, we can obtain some useful insights into the achievable error rate performance for the DQPSK modulation with Gray coding for various channel conditions in the high signal-to-noise ratio (SNR) regions.

Design and Performance Analysis of Noncoherent Detection Systems With Massive Receiver Arrays

Harvesting the gain of a large number of antennas in a mmWave band has mainly been relying on the costly operation of channel state information (CSI) acquisition and cumbersome phase shifters. Recent works have started to investigate the possibility to use receivers based on energy detection (ED), where a single data stream is decoded based on the channel and noise energy. The asymptotic features of the massive receiver array lead to a system where the impact of the noise becomes predictable due to a noise hardening effect. This in effect extends the communication range compared to the receiver with a small number of antennas, as the latter is limited by the unpredictability of the additive noise. When the channel has a large number of spatial degrees of freedom, the system becomes robust to imperfect channel knowledge due to channel hardening. We propose two detection methods based on the instantaneous and average channel energy, respectively. Meanwhile, we design the detection thresholds based on the asymptotic properties of the received energy. Differently from existing works, we analyze the scaling law behavior of the symbol-error-rate (SER). When the instantaneous channel energy is known, the performance of ED approaches that of the coherent detection in high SNR scenarios. When the receiver relies on the average channel energy, our performance analysis is based on the exact SER, rather than an approximation. It is shown that the logarithm of SER decreases linearly as a function of the number of antennas. Additionally, a saturation appears at high SNR for PAM constellations of order larger than two, due to the uncertainty on the channel energy. Simulation results show that ED, with a much lower complexity, achieves promising performance both in Rayleigh fading channels and in sparse channels.

Performance Analysis Cooperative Networks of AF over Nakagami-m Fading Channels with SC and MRC

this paper the performance of amplify and forward relay system with Maximum Ratio Combining (MRC) and Selective Combining (SC) over Nakagami-m fading channels is studied by considering both MRC and SC schemes at the destination, we derive the cumulative density function (CDF), probability density function (PDF) and moment generating function (MGF) for the multiple relay AF network with single half duplex In addition, we derive the exact Symbol Error Rate (SER) of M-ary phase-shift keying (M-PSK), in Nakagami -m fading environment. Simulation results are presented to show that system performance of the differential SC is comparable to the MRC at the receivers, and improves with the increase of repeaters, and different decoding methods have different effects on system performance. KeywordsNetworks, AF, Maximal ratio combining, Selective Combining, Nakagami -m fading channels

Performance analysis of GFDM in various fading channels

Purpose– The purpose of this paper is to study the performance of generalized frequency division multiplexing (GFDM) in some frequency selective fading channels. The exact symbol error rate (SER) expressions in Hoyt (Nakagami-q) and Weibull-vfading channels are derived. A GFDM transceiver simulation test bed is provided to validate the obtained analytical expressions.Design/methodology/approach– Modern cellular system demands higher data rates, very low-latency transmissions and sensors with ultra low-power consumption. Current cellular systems of the fourth generation (4G) are not able to meet these emerging demands of future mobile communication systems. To address this requirement, GFDM, a novel multi-carrier modulation technique is proposed to satisfy the future needs of fifth generation technology. GFDM is a block-based transmission method where pulse shaping is applied circularly to individual subcarriers. Unlike traditional orthogonal frequency division multiplexing, GFDM transmits multiple symbols per subcarrier. The authors have used the probability density function approach in solving the final analytical expressions.Findings– Detailed analysis of GFDM performance under Hoyt-q, Weibull-vand Log-Normal Shadowing fading channels. Exact analytical formulae were derived which support the simulations carried out by authors and other authors. The exact dependence of SER on fading parameters and roll-off factorαin the raised cosine pulse shape filter was determined.Practical implications– Development and fabrication of high-performance GFDM systems under fading channel conditions.Originality/value– Theoretical support to simulated system performance.

Exact SER Analysis of DFrFT-Based QPSK OFDM System over Frequency Selective Rayleigh Fading Channel with CFO

We present the exact symbol error rate (SER) expression for quadrature phase shift keying (QPSK) modulation in frequency selective Rayleigh fading channel for discrete fractional Fourier transform- (DFrFT-) based orthogonal frequency division multiplexing (OFDM) system in the presence of carrier frequency offset (CFO). The theoretical result is confirmed by means of Monte Carlo simulations. It is shown that the performance of the proposed system, at different values of the DFrFT angle parameter “α,” is better than that of OFDM based on discrete Fourier transform.

On Energy Harvesting Gain and Diversity Analysis in Cooperative Communications

The use of energy harvesting cooperative relays is a promising solution to battery-limited wireless networks. In this paper, we consider a cooperative system in which one source node transmits data to one destination with the assistance of an energy harvesting decode-and-forward (DF) relay node. Our objective is to minimize the long-term average symbol error rate (SER) performance through a Markov decision process (MDP) framework. By doing so, we find the optimal stochastic power control at the relay that adapts the transmission power to the changes of energy harvesting, battery, channel, and decoding states. We derive a finite-integral expression for the exact average SER of the cooperative system. Further insights are gained by analyzing the asymptotic average SER and its lower and upper bounds at high signal-to-noise ratio (SNR), and the performance is eventually characterized by the occurrence probability of the relay’s actions at the worst channel states in the MDP. We also show that the optimal cooperative policy at asymptotically high SNR follows a threshold-type structure, i.e., the relay spends the harvested energy only when the signal is successfully decoded and the source is faced with the worst channel condition in its direct link. Using these observations to quantify the diversity gain and the energy harvesting gain, we reveal that full diversity is guaranteed if and only if the probability of harvesting zero energy quantum is zero, which can be achieved by reducing the energy quantum size or increasing the energy harvesting capability. Finally, we present several numerical examples to validate the analytical findings.

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.