Expression For Error Probability Research Articles

Discrete time domain analysis of chaos-based wireless communication systems with imperfect sequence synchronization

Abstract Problem of sequence synchronization in chaos-based direct sequence spread-spectrum (DS-SS) systems and code division multiple access systems (CDMA) has been widely investigated. However, no mathematical expressions have been derived in closed form for the bit error probability in these systems when they operate with the imperfect time synchronization (represented by a delay between the received and reference spreading sequence generated in the receiver). Precise derivatives for this bit error probability are necessary to quantify the effect of imperfect synchronization on the overall properties of the system. To implement a random delay between the received and the receiver reference sequence, all signals in this paper are represented in the discrete time domain. To represent finite and random discrete delays between the sequences (which occur in a limited interval) the Gaussian and uniform probability density functions are expressed in discrete form. Furthermore, due to the finite value of possible random discrete delays, the expressions of related truncated density functions are expressed in closed form. Following this approach, the expressions for the bit error probability in closed form for chaotic and random spreading sequences have been derived.

Optimal ASK Levels for Channel Magnitude Based Diversity Reception in Rayleigh Fading

We consider two low-complexity receivers, namely, the energy detection (ED) receiver and the weighted envelope detection (WENVD) receiver, employing receive diversity, operating in flat Rayleigh fading with multi-level amplitude-shift keying, and having only channel magnitude information, that is, knowledge of the magnitudes of the fading gains of the receive diversity branches. A closed form expression for the approximate symbol error probability (SEP) of the WENVD receiver for high signal-to-noise ratio (SNR) is derived. Furthermore, analytical results on the optimization of the transmit symbol amplitude levels to minimize the SEP subject to a total energy constraint for high SNR and large number of receive diversity branches for both the ED and the WENVD receivers are presented. The performance improvement obtained by using these optimal levels over using symbol amplitude levels with equal spacing, that is, in arithmetic progression, for both the receivers is shown through numerical results.

On the performance of cooperative vehicular networks under antenna correlation at RSU

Vehicular communications is gradually becoming mature after decades of exciting developments and thriving advances. Resultantly, these advances have opened new possibilities for vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications to meet the requirements of safety applications and future self-driving technologies. While performance limits of single link vehicular communications have been well analyzed in the literature, only incremental growth has been shown in the domain of multi-antenna communications. Another major concern is that the existing works mostly assume independent fading at the antennas mounted on road side unit (RSU), thus neglecting the impact of channel correlation. Our work addresses this issue by evaluating packet error probability for two renowned antenna correlation models i.e., constant correlation (CC) and exponential correlation (EC), under Nakagami-m fading. We also consider cooperation between intermediate vehicles to ensure reliable communication from the source vehicle to the RSU. More specifically, we derive closed-form expressions of packet error probability for three cooperative techniques, namely, single helper selection (SHS), multi-hop cooperative selection (MCS) and multiple helper selection (MHS). We quantify the performance variations for different numbers of intermediate helper vehicles, and for varying values of fading parameter and correlation coefficients. Finally, we validate our mathematical derivations by performing extensive simulations in MATLAB.

Simultaneous wireless information and power transfer with SSK modulation over Rayleigh fading

An analysis of amplify and forward (AF) cooperative relays employing “power splitting supported energy harvesting scheme” is presented for space shift keying modulation over Rayleigh fading channels. Mathematical expressions for throughput and average bit error probability are obtained using probability density function‐based approach. Numerical and computer simulation results as a function of power splitting ratio and other system parameters are presented.

High-Diversity Joint Precoder Design for Non-Concurrent Two-Way AF MIMO Relaying

We design a precoder for non-concurrent two-way relaying (ncTWR) where a base station (BS) serves a transmit-only user equipment (TUE) in the uplink and a receive-only user equipment (RUE) in the downlink. The RUE experiences back-propagating interference (BI). The proposed precoder is designed such that it not only cancels the BI experienced by the RUE but more importantly, enables receive data decoding with high diversity. The high diversity precoder is designed by deriving the closed-form pairwise error probability (PEP) expressions, and by optimizing the precoder elements to minimize the PEP. We analytically show that with $N_{r}$ -antenna relay, $N_{b}$ -antenna BS, and $N_{u}$ -antenna TUE and RUE, both BS and RUE decode their respective data with a diversity order of $\min (N_{u}^{2},(N_{r}-N_{u})N_{b})$ at high receive signal-to-noise ratio. We also numerically show that the proposed design has lower bit error rate than the existing state-of-the-art ncTWR designs.

Error performance of Uncoded Space Time Labelling Diversity in spatially correlated Nakagami‐q channels

SummaryGreater spectral efficiency has recently been achieved for Uncoded Space Time Labelling Diversity (USTLD) systems by increasing the number of antennas in the transmit antenna array. However, due to constrained physical space in hardware, the use of more antennas can lead to degradation in error performance due to correlation. Thus, this paper studies the effects of spatial correlation on the error performance of USTLD systems. The union bound approach, along with the Kronecker correlation model, is used to derive an analytical expression for the average bit error probability (ABEP) in the presence of Nakagami‐q fading. This expression is validated by the results of Monte Carlo simulations, which shows a tight fit in the high signal‐to‐noise ratio (SNR) region. The degradation in error performance due to transmit and receive antenna correlation is investigated independently. Results indicate that transmit antenna correlation in the USTLD systems investigated (3 × 3 8PSK, 2 × 4 16PSK, 2 × 4 16QAM, and 2 × 4 64QAM) causes a greater degradation in error performance than receive antenna correlation. It is also shown that 2 × 4 USTLD systems are more susceptible to correlation than comparable space‐time block coded systems for 8PSK, 16PSK, 16QAM, and 64QAM.

The BER Analysis of MRC-Aided Greedy Detection for OFDM-IM in Presence of Uncertain CSI

This letter investigates the bit error rate (BER) performance of orthogonal frequency division multiplexing index modulation, employing the maximal ratio combining-based low-complexity greedy detector (MRC-GD) and the PSK modulation. For performance analysis, we derive tight expressions for both index error probability (IEP) and BER, taking into account channel state information (CSI) uncertainty. This provides insight into various impacts of CSI uncertainty on the diversity gain and error floor of the IEP and the BER, respectively. We clearly show that under imperfect CSI, the MRC-aided GD can perform like the MRC-maximum likelihood detector, at lower complexity. Finally, simulation results are presented to verify the accuracy of derived expressions and the theoretical analysis.

Performance analysis of shadowed-Rice fading channel with cooperative spectrum sensing

ABSTRACTIn this paper, the performance analysis of wireless communication system over shadowed-Rice (SR) composite fading channel has been investigated and analysed. The unified analytical expressions of the average symbol error probability (ASEP) for several coherent and non-coherent modulation schemes separately with different constellation sizes are derived for composite fading channel under two different fade mitigation methods, with maximal ratio combining (MRC) microdiversity (Method 1) and MRC applied over the composite fading channel (Method 2). Furthermore, an asymptotic analysis is carried out and a closed-form expression of the ASEP with Method 2 is presented. Analytical expressions of the corresponding average probability of energy detection (PD) are formulated for both the methods. Finally, the derived PD expression is utilised to analyse the performance of cooperative system assuming erroneous feedback channel. Analysis of optimisation of detection threshold as well as number of cognitive users to minimise the total error rate is also carried out. The closed-form expressions are validated by comparing them with exact numerical results and Monte Carlo simulation.

Repeated MCIK-OFDM With Enhanced Transmit Diversity Under CSI Uncertainty

This paper investigates the opportunity for a repetition coded multi-carrier index keying—orthogonal frequency division multiplexing (MCIK-OFDM), termed repeated MCIK-OFDM (ReMO), which can provide superior performance over existing schemes at the same spectral efficiency. Unlike the classical scheme, the proposed scheme activates a subset of sub-carriers and modulates them with the same $M$ -ary data symbol, while additional information is conveyed by the active sub-carrier indices. This approach not only provides the frequency diversity gains in the $M$ -ary symbol detection but also improves the index detection, leading to considerable improvement in the transmit diversity. For performance analysis, we derive tight closed-form expressions for the symbol error probability and the bit error rate, under both perfect and imperfect channel state information (CSI). These expressions provide insight into the achievable performance gains, system designs, and impacts of various CSI conditions. Finally, simulation results are given to illustrate the superior performance achieved by our scheme over existing schemes under different CSI uncertainties.

A unified performance analysis of decode‐and‐forward dual‐hop relaying‐based wireless energy harvesting with space modulation

AbstractSpace modulation techniques (SMTs) are a group of multiple‐input–multiple‐output wireless systems in which the spatial indexes of transmit antennas are utilized to convey additional information bits. The SMTs promise significant enhancements in terms of spectral and energy efficiencies and attract significant research interest in literature. Several SMTs have been proposed including spatial modulation (SM) and quadrature SM. In this study, the performance of dual‐hop decode‐and‐forward relaying SM and quadrature SM in the presence of wireless power transfer is analyzed and thoroughly discussed. Specifically, we derive exact closed‐form expressions for the pairwise error probability (PEP). In addition, we derive simple and accurate asymptotic expressions for the PEP at high signal‐to‐noise ratio, which provides insight into the influence of different system parameters. The obtained PEP expressions are then employed to evaluate the overall average bit error rate (BER). It is worth highlighting that the derived expressions are unified in the sense that they are valid for the aforementioned SMTs and for two well‐known practical energy harvesting protocols, namely, power‐splitting receiver and time‐switching receiver. In addition, we derive a unified closed‐form expressions for the outage probability and achievable throughput at the destination node. The impact of diverse system parameters, such as the power‐splitting factor, the energy‐harvesting time factor, and the distance between the source and the relay nodes, on the overall system performance is studied. The accuracy of the analytical derivations is validated through Monte Carlo simulations results.

SBL-Based Joint Sparse Channel Estimation and Maximum Likelihood Symbol Detection in OSTBC MIMO-OFDM Systems

This paper presents sparse Bayesian learning (SBL)-based schemes for approximately sparse channel estimation in an orthogonal space-time block coded (OSTBC) multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) wireless system. The parameterized prior-based SBL framework is employed to present a pilot scheme for an ill-posed OSTBC MIMO-OFDM channel estimation scenario. Maximum likelihood symbol detection (MLSD) has been incorporated in the expectation-maximization framework for SBL-based channel estimation. This has led to the development of a novel scheme for joint approximately sparse channel estimation and symbol detection. The proposed scheme performs SBL-based channel estimation in the E-step followed by a modified ML decision metric-based symbol detection in the M-step. Bayesian Cramer–Rao bounds are obtained for the genie minimum mean-squared error estimators corresponding to the SBL schemes. Closed-form bit error probability expressions are derived for the MLSD in the presence of SBL-based channel estimation errors. Simulation results are presented towards the end to validate the theoretical bounds and illustrate the performance of the proposed techniques.

Performance Analysis of Media-Based Modulation With Imperfect Channel State Information

Media-based modulation (MBM) is an attractive modulation scheme where information bits are conveyed by digitally controlling the on/off status of radio frequency mirrors (which are parasitic elements) placed near the transmit antenna. The MBM alphabet (which is the set of channel fade coefficients corresponding to all possible mirror on/off status vectors) is estimated at the receiver through pilot transmissions. In this paper, we analyze the effect of imperfect channel estimation on the bit error performance of MBM. We present the analysis for generalized spatial modulation MBM (GSM-MBM). We analyze the performance for two types of detectors, namely the commonly studied mismatched detector, and the true maximum-likelihood (ML) detector that maximizes the likelihood by taking the statistics of the channel estimate into account. First, we derive an exact average pairwise error probability (PEP) expression for the mismatched detector using characteristic function approach, and obtain a union bound based upper bound on the average bit error probability (BEP). Next, given the estimate of the MBM alphabet, we derive the true ML detector for GSM-MBM, and derive an exact average PEP expression (by averaging the conditional PEP over the statistics of the channel estimate) and an upper bound on the average BEP. The exactness of the average PEP and the tightness of the average BEP upper bounds of the detectors are validated through simulations.

Unified expressions of ASEP over Málaga ([formula omitted]) turbulence channel

In this paper, we present the unified closed-form expressions of average symbol error probability (ASEP) for both types of system (i.e. coherent and incoherent system) in the presence of pointing error over Málaga (M) turbulence channel. With the help of the approximation of exponential-type presentation of Q-function, the unified closed-form expressions are presented, which are generic enough to encompass almost all the modulation techniques of which ASEP involves the integral power of Q-function. Then, we capitalize on the results to provide the asymptotic expressions at high signal-to-noise ratio (SNR). Additionally, the diversity order and coding gain are presented, which reveal that the diversity order is depended on the channel condition and detection scheme, while the coding gain is relevant to the modulation techniques. Moreover, some special cases are presented, such as the results under Gamma–Gamma distribution and K-distribution. Numerical results corroborate the accuracy of the closed-form expressions for different modulation techniques under different turbulence conditions.

Adaptive spatial modulation and thresholds optimization for MIMO systems in correlated Rayleigh channels

Spatial modulation (SM) is a simple and spectral efficient modulation technique that has received much interest recently. In this paper, an adaptive SM (ASM) scheme is presented by combining adaptive modulation with conventional SM. The performance of ASM is analyzed in spatially correlated Rayleigh fading channels. In order to reduce the computational complexity of average bit error rate (BER), an approximate expression of error probability of the antenna index estimation, which contributes one of two components of the average BER, is derived by using the fitting method and matches well with simulation results in the SNR range of interest. With the above results, the closed-form spectrum efficiency (SE) and overall average BER are obtained, respectively. Besides, the optimized switching thresholds for maximizing SE under an average BER constraint are achieved by means of the Karush Kuhn Tucker conditions, and the resultant SE performance can be improved greatly when compared to the ASM system with fixed thresholds. Simulations indicate that the theoretical SE and BER are effective and agree well with the corresponding simulations. Moreover, the SE and BER performance of ASM under spatially correlated channel are poorer than those under spatially independent channel because of the influence of spatial correlation.

Error Analysis of SSK With Euclidean Distance Based Selection Combining

In this paper, we analyze the performance of space shift keying (SSK) modulation scheme with Euclidean distance based selection combining (ED-SC) at the receiver. This scheme utilizes a single radio frequency (RF) chain receiver that selects one out of $N_{r}$ receiver antennas based on the Euclidean distance between the SSK constellation points. In addition to this, the performance of generalized ED based SC (GED-SC) is also analyzed by utilizing two or more RF chains at the receiver. The closed form expressions for the average bit error probability (ABEP) of ED-SC and GED-SC schemes are derived for two transmit and $N_{r}$ receive antennas. Further, the theoretical ABEP analysis of ED-SC is derived for $N_{t} > 2$ . In addition to this, we also derive the diversity order analysis of ED-SC SSK system for $N_{t} = 2$ . From the diversity order analysis, it can be inferred that the diversity order obtained by the ED-SC SSK system is $N_{r}$ . It is observed from the simulation results that the performance of $2\times 4$ GED-SC SSK system with two and three RF chains is only slightly worse than the optimal detection with $N_{r}=4$ . Since only a single RF chain is utilized for signal reception in ED-SC, the receiver complexity of employing $N_{{RF}}$ RF chains in GED-SC and $N_{r}$ RF chains in optimal detection is greatly reduced. Moreover, the simulation results of the ABEP performance of ED-SC SSK system in imperfect channel state information at the receiver is shown.

On the performance of asymmetric SIM‐based RF/FSO system with MIMO DF relaying

AbstractIn this paper, we consider the asymmetric dual‐hop radio frequency (RF) and free‐space optical (FSO) wireless communication system with a decode‐and‐forward–based multiple‐input–multiple‐output relay over the Nakagami‐m/Generalized‐K( ) distribution. The distribution is a generic statistical model, which has been used for a wide range of atmospheric turbulence–induced fading in FSO communication. The coefficients of the RF hop are considered to be independent and nonidentically distributed with the Nakagami‐m distribution, and the coefficients of FSO hop are considered to be independent and identically distributed. We also consider the path loss and misalignment error effect in FSO hop. We derive the approximate closed‐form expression of the symbol error probability and outage probability in terms of the Meijer G function for the considered mixed decode‐and‐forward RF/FSO system. The closed‐form expressions of the conditional symbol error probability and outage probability are also derived for the considered system while taking into account the effect of a misalignment error. We have also analyzed the considered system for high signal‐to‐noise ratio conditions. In addition, the diversity order of the considered system is also obtained analytically.

Channel zooming for the mitigation of pilot contamination in massive MIMO

AbstractMassive multiple‐input multiple‐output is an attractive technology that aims to ameliorate both the energy and the spectrum efficiencies of fifth‐generation cellular networks. The main problem that limits the performance of a massive multiple‐input multiple‐output system is pilot contamination, which happens due to the limited number of orthogonal pilot sequences. In this paper, we assume that each cell is assigned a set of orthogonal pilot sequences and that these same pilot sequences are reused in other cells. Consequently, the contamination comes only from users in other cells, so that it is less powerful than an active user in the cell of interest. We propose a novel iterative algorithm to ensure the mitigation of the pilot contamination effect. This algorithm, dubbed as the “channel zooming algorithm”, is able to zoom through iterations on the signal of the strongest user by taking advantage of the difference in space signatures and transmitted data sequences. Moreover, we derive an analytical expression of the bit error probability, resulting after a large number of iterations of the proposed algorithm. The analytical results developed in our work are confirmed by simulation results.

Space shift keying for multi-hop multi-branch networks

In this paper, we propose two different multi-hop multiple-input multiple-output (MIMO) space shift keying (SSK) schemes and investigate their error performance. In the first scheme, we consider a multi-hop multi-branch SSK system, in which the source and destination are equipped with multiple transmit and receive antennas, respectively. In this scheme, SSK is applied by using the source transmit antennas. Moreover, in each branch, single-antenna relays are used to amplify the transmitted signal from the source and forward it to the next relay until it reaches to the destination. In the second scheme, we consider a multi-hop MIMO-SSK system with path selection. In this scheme, the best path is selected among multiple branches and a multiple-antenna source communicates with a multiple-antenna destination via the relays of the selected path. Each relay is equipped with multiple transmit and receive antennas. Moreover, the source and all relays employ SSK modulation to transmit information bits and each relay in each path follows the decode-and-forward protocol. Approximate theoretical error probability expressions are derived for both schemes. Furthermore, an asymptotic symbol error probability performance analysis is also performed for the multi-hop MIMO-SSK system with path selection. It is shown that the proposed multi-hop SSK systems outperform conventional multi-hop M-PSK systems in terms of the error performance for especially high data rates and sufficient number of receive antennas at the receiving nodes.

Analytical modeling and analysis of interleaving on correlated wireless channels

Interleaving is a mechanism universally used in wireless access technologies to alleviate the effect of channel correlation. In spite of its wide adoption, to the best of our knowledge, there are no analytical models proposed so far. In this paper we fill this void proposing three different models of interleaving. Two of these models are based on numerical algorithms while one of them allows for closed-form expression for packet error probability. Although we use block codes with hard decoding to specify the models our modeling principles are applicable to all forward error correction codes as long as there exists a functional relationship (possibly, probabilistic) between the number of incorrectly received bits in a codeword and the codeword error probability. We evaluate accuracy of our models showing that the worst case prediction is limited by 50% across a wide range of input parameters. Finally, we study the effect of interleaving in detail demonstrating how it varies with channel correlation, bit error rate and error correction capability. Numerical results reported in this paper allows to identify the optimal value of the interleaving depth that need to be used for a channel with a given degree of correlation. The reference implementations of the models are available [1].

Application of best relay selection approach to cooperative DF IDMA systems over Rayleigh/Weibull fading channels

SummaryThis paper analyzes the performance of cooperative decode‐and‐forward (DF) interleave‐division multiple‐access (IDMA) networks with best relay selection over Rayleigh/Weibull fading environments. In the analysis, approximate outage probability (OP) and bit error probability (BEP) expressions are derived for the considered system. Further, a 2‐hop DF IDMA system is also designed to compare with cooperative one. We propose OP and BEP expression for 2‐hop DF IDMA systems. Numerical results are obtained by changing the number of relays and the value of fading parameter in the proposed expressions. Also, simulations are provided to corroborate the exactness of the derived approximate OP and BEP expressions.