Amplify-and-Forward Relaying with Optimal and Suboptimal Transmit Antenna Selection

This paper investigates the performance of a two-way decode-and-forward (DF) multi-antenna relay network. A joint antenna selection scheme for all nodes is first proposed based on the maximizing the worse received signal to noise ratio (SNR) of two end users. Then, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the received SNRs of both users. We also achieve the closed-form expressions of average bit error rate (BER) and outage probability of the relay system. Furthermore, we reveal the asymptotic behavior of our system when transmitting SNR or the number of antennas is large. Our analysis shows that the proposed DF antenna selection scheme achieves full diversity. The numerical results finally verify the accuracy of our analysis.

Euclidean distance optimized antenna selection (EDAS) has proven to be able to achieve high transmit diversity gains for spatial modulation (SM) multiple-input multiple-output (MIMO) systems, but the exhaustive search over all possible antenna subsets may result in an intractable search complexity, especially for large-scale MIMO (LS-MIMO) systems. In this paper, a novel EDAS-equivalent criterion, relaying on matrix dimension reduction, is proposed to reduce the search complexity. Based upon this criterion, for small-scale SM-MIMO systems, a pair of transmit antenna selection (TAS) schemes, namely, the tree search based antenna selection (TSAS), and the decremental antenna selection (D-AS) schemes, are developed. Specifically, the TSAS scheme works by iteratively splitting the original Euclidean distance (ED) matrix into submatrices with smaller dimensions. TSAS achieves the same bit error rate (BER) performance as that of the exhaustive search at the cost of exponential search complexity. To address this issue, D-AS is carried out by excluding one specific transmit antenna from all the possible candidates in each iteration based on the channel information. D-AS is able to offer a near-optimal BER performance with a further reduction in terms of the search complexity. Moreover, we extend the D-AS scheme to LS-SM-MIMO systems by sorting all the ED elements with the low-complexity heapsort algorithm. Our simulation results show that the proposed D-AS algorithm outperforms conventional TAS schemes conceived for LS-SM-MIMO systems.

The performance analysis of multiuser multiple-input multiple-output (MIMO) system with rate-adaptive modulation and antenna selection over Rayleigh fading channels is presented. By means of exact expression of bit error rate (BER), the suboptimal switching thresholds (ST) of fading gain subject to a target BER constraint are derived. It is shown that this suboptimal ST are very close to the optimal ST, and is more accurate than the conventional ST based on approximate BER expression. By the ST, we obtain exact closed-form expressions of the spectrum efficiency (SE) and average BER. Moreover, a tightly approximate BER is derived to simplify the calculation of exact BER, which has more accuracy than the existing approximate BER. Simulation results for SE and BER are in good agreement with the derived theoretical expressions. The results show that the multiuser MIMO with adaptive modulation can provide better SE than the single user counterpart, and the system SE using suboptimal ST is also higher than that using conventional ST.

By combing Spatial modulation (SM) with the Amplify-and-forward (AF) cooperative communication, a cooperative SM scheme with AF (AF-SM) protocol is presented, and the corresponding Bit error rate (BER) performance is investigated. Based on the performance analysis, the error probability of antenna index estimation ( P a ) and the error probability of symbol estimation ( P d ), which constitutes the overall average BER, are derived, respectively. As a result, tightly approximate closedform expressions of P a and P d are attained, respectively. Using these expressions, the closed-form overall average BER is achieved. During the analysis, the computational complexity of AF-SM detector is also provided in terms of the complex addition and multiplication numbers. Besides, the asymptotic BER at high SNR and the corresponding diversity gain are further derived, and the resultant diversity gain of N r + 1 is obtained for the system with N r receive antennas. Simulation results show that our theoretical analysis is valid, and provides good performance evaluation method for cooperative SM system. Moreover, the BER performance can be effectively improved as N r increases due to higher diversity gain.

In this paper, switch-and-stay combining (SSC) is considered in two-way relay systems with amplify-and-forward (AF) relays, among which one is activated to assist the information exchange between two sources. We assume that the two-way relay system operates in the analog network coding (ANC) protocol where the communication can only be achieved through the active relay without the direct link. The outage probability and the average bit error rate (BER) for Rayleigh fading channels are studied. In particular, we derive closed-form lower bounds for the outage probability and the average BER, which is tight for different fading conditions. Moreover, we present asymptotic analysis for both the outage probability and the average BER at high signal-to-noise ratio (SNR) region. It is shown that SSC can achieve the full diversity order in two-way relay systems with proper switching thresholds. Numerical and simulation results are also provided to verify the theoretical study.

We investigate the effects of correlation on the performance of diversity systems in wideband wireless radio environments. Specifically, the average bit error rate (BER) performance of M-ary differential phase shift keying (MDPSK) on correlated frequency-selective slow Rayleigh fading channels is analyzed. A two-branch diversity receiver with postdetection equal gain combining is considered. Nyquist pulse shaping is used and differential detection is employed at the receiver. The effects of cochannel interference on the system performance are assessed using a Gaussian interference model. To further enhance the system performance, the effects of combined diversity and forward error correction (FEC) coding on the average BER are investigated. Results using short cyclic block codes with perfect bit interleaving are obtained. The effects of the root mean square (RMS) delay spread, the amount of correlation, and the level of modulation, M, on the average BER are investigated in detail for both coded and uncoded systems. The results show that dual branch diversity combining with a correlation coefficient of 0.5 outperforms (in terms of BER) short block codes with perfect bit interleaving, and that combined diversity and coding strategies are effective in combatting the effects of frequency-selective fading.

Average Bit Error Rate (BER) expression of free-space optical (FSO) communication links with Airy beam as signal carrier under weak atmospheric turbulence and on–off keying modulation scheme is derived based on scintillation index of Airy beam and Exponentiated Weibull channel model. The average BER has been evaluated at different transverse scale factors and exponential decay factors of Airy beam and link distances. And comparison of the average BER of FSO links with Airy beam and Gaussian beam as signal carrier has been carried out. The simulation results show that the average BER of FSO links with Airy beam as carrier decreases with the increase of mean signal to noise ratio and increases with the increase of transmission distance. When the transverse scale factor is about 1.5 cm, a lower average BER can be obtained. And the smaller the exponential decay factor is, the lower the average BER is. Under the same atmospheric turbulence condition, the average BER of FSO links with Airy beam as carrier is obviously better than that of FSO links with Gaussian beam as carrier. The results of this research have some significance for the application of Airy beam in FSO system.

Composite fading models have been considered as the suitable fading models for scenarios such as indoor communication and free space optical. Most of the composite fading models are based on Nakagami-m fading distribution in which amount of fading parameter ranges from 0.5 (most severe fading) to infinity (no fading). However, using the McKay–Meijer G function, one of the recent article presents McKay shadowed fading distribution which shows that the fading severity may have values more than that of the most severe case of Nakagami-m fading. In this paper, using the conditional unified expression for conditional bit error rate (BER), a unified expression of the average bit error rate (ABER) over McKay–Meijer G shadowed fading model has been proposed. The proposed unified expression includes the ABER of almost all the modulation schemes. In addition, expression for ABER of binary phase shift keying modulation over McKay fading channel under generalised Gaussian distribution has been derived. Finally, analytical expressions of adaptive capacity under different adaptive schemes namely, COPRA, CORA, CCIFR and truncated CIFR have been presented. Through numerical analysis, different results have been compared with similar results available in the literature.

High speed integrated RF–VLC data communication system: Performance constraints and capacity considerations

In this paper, the error performance analysis of an amplify-and-forward (AF) relay-aided cooperative multi-antenna system using spatial modulation (SM) over Rayleigh channels is presented. The SM is a simple and spectral efficient modulation technique that can increase the data rate by using input data bits to select a transmit antenna to send a constellation point. The relay transmission deploying SM not only can enhance the coverage and but also can improve the spectral efficiency. In the performance analysis, the overall average bit error rate (BER), which is related to the error probability of an antenna index detection ( $P_{a}$ ) and the error probability of symbol detection ( $P_{d}$ ) given transmit antenna index, is analyzed. With the derivation of the probability density function and the moment generating function of output signal-to-noise ratio (SNR), closed-form expressions of $P_{a}$ and $P_{d}$ are obtained to compute the overall BER. With the obtained BER expression, asymptotical BER expressions are derived to reveal the BER performance of the system at high SNR. By minimizing the asymptotical BER, a suboptimal power allocation (PA) scheme is developed. The diversity gain is analyzed at high SNR. The results indicate that the cooperative AF-SM can achieve full diversity order. Simulation results verify the effectiveness of the theoretical BER analysis, and the cooperative AF-SM with PA scheme outperforms upon the equal PA scheme.

Recently massive MIMO systems have attracted a lot of attention. A serious limitation in implementing massive MIMO is the number of RF chains required, which is due to its high implementation cost and power consumption. Antenna selection is a wise remedy, that not only reduces the number of required RF chains, but also improves the system’s performance. In this work, two low complexity capacity-maximizing transmit antenna selection (TAS) schemes, one for low SNR region and one for medium to high SNR region, are proposed. It is shown that the proposed antenna selection schemes enhance the MIMO link’s capacity at low SNRs, and select only one antenna in more than $$90\%$$ of channel realizations, which in terms of numbers of required RF chains is very promising. The performance of the proposed schemes are compared to an existing high performance greedy TAS technique in terms of average capacity and complexity. Finally, a close analytical approximation for average capacity of the proposed capacity-based subset selection scheme is presented.

In this paper, we analyze the average bit error rate (BER) and outage probability performances of a free-space optical (FSO) system. We used M-ary amplitude shift keying modulation (M-ary ASK) scheme. Lognormal atmospheric turbulence with the effect of pointing errors (PE) and, path loss is employed to model the FSO channel. However, to overcome the degradation in BER performance due to pointing errors, the single-input-multiple-output technique with maximal ratio combining diversity is used. For instance, the average BER for M=2 without using SIMO is 1.944×10−6 at 0 dBm transmitted power, while the average BER for M=2 with using SIMO technique with N=2 become 1.512×10−11 at 0 dBm. The asymptotic expression for average BER and the closed-form expression for outage probability are both driven and tested with and without SIMO.

Outage analysis for joint antenna and path selection decode-and-forward relay networks

This paper presents simple, exact, and closed-form expressions for the average bit error rate (BER) of M-ary orthogonal signals with noncoherent diversity combining over independent as well as arbitrarily correlated nonidentically distributed Nakagami-m fading channels. The fading channels are allowed to have arbitrary average signal-to-noise ratios (SNRs) as well as arbitrary fading parameters. The derived expressions are given in terms of elementary functions, they do not involve numerical integrals or complicated functional operations, and can easily be evaluated numerically. The results show that the system average BER can be estimated using the derived expressions herein with large computational time savings as compared with those taken by the ones addressed perviously.

This paper presents a detailed study for indoor wireless environments, where transmit power, rate and target bit error rate (BER) are varied to increase spectral efficiency. The study is conducted for the recently proposed joint fading and two-path shadowing (JFTS) channel model, which is shown to be accurate for modeling non-Gaussian indoor WLAN environments. Analysis is done for both average and instantaneous BER constraints without channel coding, where only a discrete finite set of constellations is available. Numerical results show that, for a JFTS channel i) varying only the transmission rate (modulation constellation size) achieves more improvement in spectral efficiency compared to varying transmit power only, and ii) varying rate and/or power subject to instantaneous BER (I-BER) constraint offers better performance than when subject to average BER (A-BER) constraint.