Average Bit Error Probability Research Articles

Performance Analysis of Spatial Modulation Under Rapidly Time-Varying Rayleigh Fading Channels

Due to the problem of inter-channel interference, the average bit error probability (ABEP) performance of the traditional multiple transmit and multiple receive antenna systems obviously deteriorates. A promising scheme to address this issue is the spatial modulation (SM) which activates only one transmit antenna at each signaling period. In addition, the demand to provide data services for high mobility users is ever increasing, where fading channels are more likely to be rapidly time-varying. Therefore, in this paper, we investigate the ABEP performance of SM under the assumption that system’s fading channels are Rayleigh and varying from one signaling period to another within the same transmitted data block. Further, to simplify the decoding complexity at the receiver, the channel is assumed to be estimated at the first location of each data block and then used to detect the received symbols at the remaining locations of the block. For such a system, and unlike other literature works, we derive novel, exact and closed-form reduced enough expressions for the average pairwise error probabilities (average-PEPs), which are then used to compute the system’s overall per-block ABEP efficiently. The derived expressions are generic and valid for both time-varying and slow fading environments. Furthermore, the obtained analytical results are exploited to quantitatively show that the time-varying fading environment degrades the SM system’s performance through irreducible error floors. Numerical and simulation results of various examples are provided to validate the theoretical analyses and also to get some insights into the effect of the different system parameters (such as the speed of the mobile, the carrier frequency, and the block size of the channel variations) on the overall SM error performance.

Bit allocation approach of spatial modulation for multi-user scenario

In this study, a multi-user bit allocation approach using spatial modulation (SM) technique is proposed. Massive connectivity can be covered using the proposed scheme such as for massive downlink (DL) internet of things (IoT). In the proposed scheme, like single-user DL SM, a single antenna is activated to send information to multiple DL users. At each user, the antenna index and constellation symbol are then estimated and converted into information bits. The information bits are extracted to obtain bits that are addressed only to the particular user. Consequently, both inter-channel and inter-user interference can be avoided among the users in the proposed scheme. As performance measures, average bit error probability (ABEP) and throughput are evaluated. It is shown that the ABEP of each user in the proposed scheme outperforms that in a single-user DL SM system by both analysis and simulation. The throughput analysis also shows that overall throughput of proposed system outperforms that in a single-user DL system. Moreover, the receiver complexity comparison between the existing technique with the proposed scheme for multi-user is presented. It is shown that the proposed system achieves the lowest receiver complexity compared to the others with the same system configurations. Finally, the energy efficiency comparison with the existing technique is also presented. It shown that the proposed system achieves lower energy consumption compared with the existing technique.

Impact of symmetric and asymmetric fading channels on dual-hop AF relay system with SSK modulation

Performance of dual-hop amplify-and-forward relaying system is analyzed over asymmetrical Nakagami-m/Rcian and symmetrical Nakagami-m/Nakagami-m fading channel with space shift keying (SSK) modulation. Expressions for average bit error probability (ABEP) of SSK modulation scheme over the line-of-sight and non-line of sight fading channels have been obtained. Analytical expressions for cumulative distribution function of the end-to-end signal-to-noise ratio are derived and a mathematical expression for the ABEP of SSK modulation is obtained for both in presence of the direct link between source to destination and in absence of the direct link. The derived expressions are given in terms of the Whittaker functions and Gamma functions. ABEP expressions are also derived which provide useful insights into the factors governing the performance of the considered system. The numerical results have been verified with Monte-Carlo simulation results.

Space shift keying modulation under spectrum sharing over Nakagami‐m fading

In this letter, we analyze the performance of the space shift keying (SSK) modulation scheme for underlay spectrum‐sharing environments. For underlay spectrum‐sharing transmission, the transmit power condition of the proposed spectrum‐sharing system is considered by the interference temperature limit on the primary network and the maximum transmission power at the secondary network. Closed‐form expression for the average bit error probability (ABEP) is derived for Nakagami‐m fading channels. The obtained expression contains a hypergeometric function. Numerical and simulation results are presented to illustrate the impact of the fading parameters on the system performance.

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.

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.

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.

Performance Analysis of MMSE Pre-Coding Aided Spatial Modulation

Pre-coding aided spatial modulation (PSM) constitutes a flexible closed-loop multiple-input multiple-output transmission scheme, which attracts substantial research interest recently. In this paper, an upper bound of the average bit error probability (ABEP) for the PSM system based on the minimum mean square error (MMSE) pre-coding is investigated. In addition, a theoretical analysis is given based on the assumption that the numbers of transmit and receive antennas are large but their ratio $\theta $ is constrained. Furthermore, the theoretical analysis shows that the ABEP upper bound of the PSM system based on MMSE pre-coding depends only on ratio $\theta $ . Simulation results demonstrate that the upper bound is asymptotically tight as the signal-to-noise ratio increases, and the proposed system outperforms its benchmark that is based on zero-forcing pre-coding.

An Accurate, Fast Approximation for the Sum of Fading Random Variables via Expectation Maximization Applications to Diversity Systems

Sums of fading envelopes occur in several wireless communications applications. The exact mathematical solution to this statistic is, however, rather intricate. In this paper, we derive a novel closedform approximation to the sum of not necessarily identically distributed Nakagami-m random variables. The necessary parameters of the approximate solution are estimated by using the well-known expectation maximization algorithm with a Nakagami-m mixture model. The proposed approximation finds applicability in obtaining important performance metrics of communications systems where sums of variates arise. More specifically, we apply the proposed method to derive a closed-form expression for average bit error probability (ABEP) of multibranch equal-gain combining receivers. The presented models are general and can be applied to any modulation scheme. Furthermore, simplified asymptotic closed-form expressions for the ABEP have been derived to examine the achievable diversity and coding gains. Finally, the performance of the proposed approach is verified by comparing itself against both the exact evaluation and the previous results in the literature.

Experimental analysis and comparison of tropospheric scintillation prediction models using eutelsat-36b satellite in a tropical Nigeria

Knowledge on clear-air effects is of paramount importance to proper link budgeting for optimum communication systems design performances. In this paper, one-year (January - December 2013) tropospheric scintillation data are extracted from the EUTELSAT-36B Ku-band satellite measurements installed at Akure (Lat: 7.17 oN, Long: 5.18 oE, Alt: 358 m) for statistical analysis and the result compared with some established troposphere scintillation models in order to obtain the best prediction model performance for this region. The result shows that even in the absence of rain, tropospheric scintillation shows a strong seasonal effect in this region up to amplitude above 0.92 dB. The scintillation intensity fits better to gamma distribution at a high scintillation level taken into consideration the local meteorological parameters. Models comparison with experimental data also shows that the Karasawa model with the lowest percentage error of about 7% was found to be best fit for predicting propagation impairment relating to be fading at a Ku band frequency in this region. The overall results will provide information on scintillation margin needed for sizing antennas and amplifiers for reliable performance and the average bit-error probability on a scintillation-degraded digital satellite link in this region.

Signal constellations employing multiplicative groups of Gaussian and Eisenstein integers for Enhanced Spatial Modulation

In this paper, we propose two new signal constellation designs employing Gaussian and Eisenstein Integers for Enhanced Spatial Modulation (ESM). ESM is a novel technique which was propounded by Cheng et al. The advantage of ESM over other Spatial Modulation (SM) schemes lies in its ability to enhance spectral efficiency while keeping the energy efficiency intact. This is done by activating either one or two antennas judiciously depending upon the required trade-off. In ESM, information radiated from the antennas depends upon index of the active transmit antenna combination(s) and also on the set of constellation points chosen, which may include points from multiple constellations. In this paper, we propose signal constellations based on multiplicative groups of Gaussian and Eisenstein integers. The set comprising of Gaussian and Eisenstein integers serves as primary and secondary constellation points for Gaussian Enhanced Spatial Modulation (GESM) scheme. The secondary constellation points are deduced from a single geometric interpolation from the primary constellation points. The Monte Carlo simulation results indicate that the proposed nonuniform constellations achieve impressive SNR gains compared to conventional constellation points used in the design of ESM. This new design has been described for MIMO employing 4 × 4 and 8 × 8 antenna configurations with only two active antennas. Furthermore, a closed form expression for the pairwise error probability (PEP) for the GESM scheme has been deduced. The PEP is utilized to determine the upper bound on the average bit error probability (ABEP). Our simulations indicate that the proposed GESM from Gaussian and Eisenstein integers scheme outperforms all the other variants of SM including conventional ESM by at least 2.5 dB at an average bit error ratio (ABER) of 10−5. Close correspondence between the theoretical analysis and the Monte Carlo simulation results are observed.

A comprehensive framework for Double Spatial Modulation under imperfect channel state information

The essential requirement for a 5G wireless communication system is the realization of energy efficient as well as spectrally efficient modulation schemes. Double Spatial Modulation (DSM) is a recently proposed high rate Index Modulation (IM) scheme, designed for use in Multiple Input Multiple Output (MIMO) wireless systems. The aim of this scheme is to increase the spectral efficiency of conventional Spatial Modulation (SM) systems while keeping the energy efficiency intact. In this paper, the impact of imperfect channel knowledge on the performance of DSM system under Rayleigh, Rician and Nakagami-m fading channels has been quantified. Later, a modified low complexity decoder for the DSM scheme has been designed using ordered block minimum mean square error (OB-MMSE) criterion. Its performance under varied fading environments have been quantified via Monte Carlo simulations. Finally, a closed form expression for the pairwise error probability (PEP) for a DSM scheme under conditions of perfect and imperfect channel state information has been derived. This is employed to calculate the upper bound on the average bit error probability (ABEP) over aforementioned fading channels. It is observed that, under perfect and imperfect channel conditions DSM outperforms all the other variants of SM by at least 2dB at an average bit error ratio (ABER) of 10−5. Tightness of the derived upper bound is illustrated by Monte Carlo simulation results.

Polarization Shift Keying (PolarSK): System Scheme and Performance Analysis

Single-Radio-Frequency (RF) Multiple-Input-Multiple-Output (MIMO) systems such as the spatial modulation (SM) system and the space shift keying (SSK) system have been proposed to pursue a high spectral efficiency while keeping a low cost and complexity transceiver design. Currently, polarization domain resource has been introduced to the single-RF MIMO system to reduce the size of the transmit antenna array and provide 1 bit per channel use (bpcu) multiplexing gain. Nevertheless, the polarization domain resource still has the potential to provide a higher multiplexing gain in the polarized single-RF MIMO system. In this paper, we propose a generalized polarization shift keying (PolarSK) modulation scheme for a SIMO system that uses the polarization states in the dual-polarized transmit antenna as an information-bearing unit to increase the overall spectral efficiency. At the receive end, the maximum likelihood (ML) detector is employed to demodulate the received signal. A closed form union upper bound on the average bit error probability (ABEP) of PolarSK system with the optimum maximum likelihood (ML) receiver is deduced under fading channels. To reduce the computational complexity of the receiver, a linear successive interference cancellation (SIC) detection algorithm and a sphere-decoding (SD) detection algorithm are proposed. On the basis of analytic results and simulations, performances of the proposed PolarSK systems in terms of computational complexity and ABEP are analyzed. Numerical results show that the proposed PolarSK scheme performs better than state of the art dual-polarized/uni-polarized SM schemes.

Quadrature spatial media‐based modulation with RF mirrors

The use of radio frequency (RF) mirrors to improve spectral efficiency is a recently introduced technique. The authors investigate its application to single RF chain and inter-channel interference-free communications. The technique is first applied to improve the error performance of a conventional single-input multiple-output (SIMO) scheme, in the form of SIMO media-based modulation (SIMO-MBM) with single-mirror activation pattern (MAP). Significant improvement in error performance is demonstrated. The theoretical average bit error probability (ABEP) of SIMO-MBM with single MAP is formulated and serves to validate the Monte-Carlo simulation results. The application of RF mirrors to further improve spectral efficiency in quadrature spatial modulation is then proposed, in the form of quadrature spatial media-based modulation (QSMBM) and is able to achieve very large spectral efficiencies, while maintaining relatively good error performance. The theoretical ABEP of QSMBM is formulated and shown to agree well with Monte-Carlo simulation results. Finally, MAP selection for QSMBM is investigated. Due to the high computational complexity and memory requirements of optimal MAP selection, low-complexity suboptimal algorithms for MAP selection are investigated. A significant improvement in the error performance of QSMBM is demonstrated with these algorithms.

Investigation into diversity order at micro and/or macro level in gamma shadowed Nakagami‐m fading channels

AbstractRadio wave propagation through wireless channels is characterized by 4 main physical phenomena: reflection, diffraction, scattering, and absorption. Considerable efforts have been devoted to develop precise mathematical description of signal fluctuations which is very helpful in designing and evaluating the performance of wireless communication systems. A space diversity reception technique presents effective method for increasing channel capacity and upgrading transmission reliability at relatively low cost. In this paper, wireless communication system with maximal‐ratio combining (MRC) microdiversity and selection combining (SC) macrodiversity reception operating over correlated gamma shadowed Nakagami‐m fading channels is studied. Average bit error probability (ABEP), outage probability and average channel capacity, being significant and generally adopted performance measures, are employed to investigate how system performance is affected by the number of base stations and the number of antennas per base station.

Redesigned Spatial Modulation for Spatially Correlated Fading Channels

In this paper, a new variant of Spatial Modulation (SM) Multiple-Input Multiple-Output (MIMO) transmission technique, designated as Redesigned Spatial Modulation (ReSM) has been proposed. In ReSM scheme, a dynamic mapping for antenna selection is adopted. This scheme employs both single antenna as well as double antenna combinations depending upon channel conditions to combat the effect of spatial correlation. When evaluated over spatially correlated channel conditions, for a fixed spectral efficiency and number of transmit antennas, ReSM exhibits performance improvement of at least 3 dB over all the conventional SM schemes including Trellis Coded Spatial Modulation (TCSM) scheme. Furthermore, a closed form expression for the upper bound on Pairwise Error Probability (PEP) for ReSM has been derived. This has been used to calculate the upper bound for the Average Bit Error Probability (ABEP) for spatially correlated channels. The results of Monte Carlo simulations are in good agreement with the predictions made by analytical results. The relative gains of all the comparison plots in the paper are specified at an ABER of 10−4.

On the SINR statistics of a VFDM cognitive spectrum sharing system

An analytical precise approximation of the SINR statistics of the two-tier Vandermonde-subspace frequency division multiplexing (VFDM) cognitive spectrum sharing systems over frequency-selective Rayleigh fading channels is presented. It is shown that the gamma distribution provides the best fitting accuracy and that its use leads to simple, yet accurate, closed-form expressions for evaluating the ergodic capacity (EC) and average bit error probability (ABEP) performance of such systems. In deriving these expressions, the parameters of the gamma distribution have been obtained for various operating conditions of the considered VFDM system using distribution fitting. Furthermore, regression analysis has been used to obtain approximate analytical expressions for these parameters in relation to the system operating parameters. Performance evaluation results, obtained for various system implementations, including the standardized IEEE 802.11 and 3GPP LTE, are presented to demonstrate the validity of the proposed methodology. Its accuracy has been verified by means of computer simulations.

Asymptotically Optimal Power Allocation for Energy Harvesting Communication Networks

For a general energy harvesting (EH) communication network, i.e., a network where the nodes generate their transmit power through EH, we derive the asymptotically optimal online power allocation solution that optimizes a general utility function when the number of transmit time slots, $N$ , and the battery capacities of the EH nodes, $B_{\rm max}$ , satisfy $N\rightarrow \infty$ and $B_{\rm max}\rightarrow \infty$ . The considered family of utility functions is general enough to include the most important performance measures in communication theory, such as the average data rate, outage probability, average bit-error probability, and average signal-to-noise ratio. The proposed power allocation solution is very simple. Namely, the asymptotically optimal power allocation for the EH network is identical to the optimal power allocation for an equivalent non-EH network whose nodes have infinite energy available but their average transmit power is constrained to be equal to the average harvested power and/or the maximum average transmit power of the corresponding nodes in the EH network. Moreover, the maximum average performance of a general EH network converges to the maximum average performance of the corresponding equivalent non-EH network, when $N\rightarrow \infty$ and $B_{\rm max}\rightarrow \infty$ . Although the proposed solution is asymptotic in nature, it is applicable to EH systems transmitting in a large but finite number of time slots and having a battery capacity much larger than the average harvested power and/or the maximum average transmit power.

Performance of Space-Shift Keying With Buffer-Aided Amplify-and-Forward Relaying

In this paper, we study a space-shift keying (SSK) based dual-hop relaying system. We assume that the relay node (RN) possesses an information buffer and propose an adaptive transmission scheme in which the system adaptively chooses the source–relay or the relay–destination links to transmit information in each time slot. We obtain an exact closed-form expression of the average bit-error probability for the system in which the source node has two transmit antennas. For the system with arbitrary number of transmit antennas, an upper bound is provided, and it is shown that the proposed scheme can achieve a diversity order of two by using the asymptotic analysis. The delay of the information packets at the RN is investigated, and two link adaptation schemes are proposed to reduce the average packet delay. Numerical results validate our analysis and show that the proposed scheme can significantly improve the system performance, as compared to the conventional relaying scheme.

Performance analysis of OOK-based FSO systems in Gamma–Gamma turbulence with imprecise channel models

For an FSO communication system with imprecise channel model, we investigate its system performance based on outage probability, average BEP and ergodic capacity. The exact FSO links are modeled as Gamma–Gamma fading channel in consideration of both atmospheric turbulence and pointing errors, and the imprecise channel model is treated as the superposition of exact channel gain and a Gaussian random variable. After we derive the PDF, CDF and nth moment of the imprecise channel gain, and based on these statistics the expressions for the outage probability, the average BEP and the ergodic capacity in terms of the Meijer’s G functions are obtained. Both numerical and analytical results are presented. The simulation results show that the communication performance deteriorates in the imprecise channel model, and approaches to the exact performance curves as the channel model becomes accurate.