Finite-SNR analysis for partial relaying cooperation with channel coding and opportunistic relay selection

This work studies the performance of a cooperative network which consists of two channel-coded sources, multiple relays, and one destination. Due to the spectral efficiency constraint, we assume that a single time slot is dedicated to relaying. Conventional network-coded based cooperation (NCC) selects the best relay which uses network coding to serve the two sources simultaneously. It is shown that NCC, however, only achieves diversity of order two regardless of the number of available relays and the channel code. In this paper, we propose a novel partial relaying based cooperation (PARC) scheme to improve the system diversity in the finite signal-to-noise ratio (SNR) regime. Firstly, closed-form expressions for the system bit error rate (BER) and diversity order of PARC are derived as a function of the operating SNR value and the minimum distance of the channel code. Secondly, we analytically show that the proposed PARC achieves full diversity order in the finite SNR regime, given that an appropriate channel code is used. Finally, numerical results verify our analysis and demonstrate a large SNR gain of PARC over NCC in the SNR region of interest.

This paper presents theoretical and experimental bit error rate (BER) results for a freespace optical (FSO) multiple-input-multiple-output system over an arbitrarily correlated turbulence channel. We employ an erbium-doped fiber amplifier at the receiver (Rx), which results in an improved Rx's sensitivity at the cost of an additional non-Gaussian amplified spontaneous emission noise. Repetition coding is used to combat turbulence and to improve the BER performance of the FSO links. A mathematical framework is provided for the considered FSO system over a correlated non-identically distributed Gamma-Gamma channel; and analytical BER results are derived with and without the pre-amplifier for a comparative study. Moreover, novel closed-form expressions for the asymptotic BER are derived; a comprehensive discussion about the diversity order and coding gain is presented by performing asymptotic analysis at high signal-to-noise ratio (SNR). To verify the analytical results, an experimental set-up of a 2 x 1 FSO-multiple-input-single-output (MISO) system with pre-amplifier at the Rx is developed. It is shown analytically that, both correlation and pre-amplification do not affect the diversity order of the system, however, both factors have contrasting behaviour with respect to coding gain. Further, to achieve the target forward error correction BER limit of 3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , a 2 × 1 FSO-MISO system with a pre-amplifier requires 6.5 dB lower SNR compared with the system with no pre-amplifier. Moreover, an SNR penalty of 2.5 dB is incurred at a higher correlation level for the developed 2 × 1 experimental FSO set-up, which is in agreement with the analytical findings.

The performance analysis of a space–time block coded multiple input multiple output system with variable-power (VP) adaptive modulation (AM) over Rician fading channels for imperfect channel state information is presented. The optimum switching thresholds for attaining maximum spectrum efficiency (SE) subject to a target bit error rate (BER) and an average power constraint are derived. In the derivation, a very tight BER expression of quadrature amplitude modulation (QAM) is used to develop a new power adaptation scheme that can fulfil the target BER even at low signal-to-noise ratio (SNR) and achieve higher SE than the scheme using the BER upper bound commonly adopted in the literature. The existence and uniqueness of the Lagrange multiplier used in the constrained optimisation are investigated. It is shown that the Lagrange multiplier is unique when it exists. By using the switching thresholds, the authors obtain closed-form expressions of SE and average BER of the system. Computer simulation shows that the theoretical analysis is in good agreement with simulation. The results show that the proposed VP-AM scheme provides better SE than the constant-power counterparts and the VP-AM scheme using the commonly used BER bound.

In contrast with orthogonal multiple access (OMA) technologies, non-orthogonal multiple access (NOMA) technology can achieve higher spectral efficiency and support more users simultaneously. Multiple relays can be deployed in NOMA networks, in order to combat fading and thus increase the transmission reliability. In the existing works on cooperative NOMA networks with multiple relays, the decoding error at the relays and the imperfect successive interference cancellation (SIC) are not taken into account simultaneously. In this work, we consider the bit error rate (BER) analysis of relay-aided NOMA networks, where max-min relay selection is employed. Particularly, closed-form BER expressions are derived for NOMA networks with Rayleigh fading, in the existence of the relay decoding error and imperfect SIC. The asymptotic BER performance is then obtained to provide some useful insights into the system design such as the diversity order. Finally, simulation results illustrate the correctness of the derived expressions. The presented results reveal the effects of imperfect SIC and relay decoding error on the performance of cooperative NOMA networks.

In free space optical (FSO) communication systems, atmospheric turbulence is the major cause of bit error rate (BER) performance degradation. The error performance of the system can be significantly improved with the help of spatial diversity by employing multiple transmit or receive apertures. However, correlation of channels under turbulence in the case of small separation between transmit apertures can substantially reduce the benefits of spatial diversity. Still, a thorough analysis of the system performance in terms of diversity order and coding gain for the FSO multiple-input single-output (MISO) system under turbulence influenced correlated channels has not been studied when the repetition coding is used to achieve improved BER performance. In this paper, we provide unique results of the BER performance analysis of the considered correlated FSO-MISO system over Gamma–Gamma distributed turbulence channel. Using the joint moment generating function of received signal-to-noise ratio (SNR), a novel generalized approximate BER expression is derived, followed by convergence test of the power series based BER expression using the Cauchy's ratio test. Then, an asymptotic analysis at high SNR is performed to obtain a novel closed-form expression for BER of FSO-MISO system. We also derive expressions for coding gain, diversity gain, and coding gain loss due to correlation in channels. Although the effect of correlation in channels on the BER performance of the system is analyzed under different scenarios, while it is observed that it does not affect the diversity order; it significantly degrades the coding gain of the considered system.

We consider very general code-division-multiple-access (CDMA) systems, namely multiple-chip-rate CDMA systems, where signals can be transmitted at different chip rates, carrier frequencies, processing gains, and transmitted powers to satisfy the given quality of service (QoS) requirements. Also, non-zero and possibly different carrier frequency offsets are assumed for different users. For these systems, a closed-form bit error rate (BER) expression is derived based on the simplified improved Gaussian approximation. Unlike the conventional simplified improved Gaussian approximation, however, we utilize the correlations between chip waveforms and their integrations rather than using the correlations between chip sequences in order to obtain the closed-form BER expression. Numerical results demonstrate that the proposed method provides much more accurate BER values compared to the standard Gaussian approximation

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.

In this paper, we propose and analyze a multihop transmission scheme based on detect-and-forward (DF) relay protocol and network coding (NC) for two-way relay channels. In this scheme, the odd relays perform hard detection and then forward the detected signals to the next hop, whereas the even relays perform NC on the detected signals from the two adjacent nodes and broadcast them to the next hop. By separating the network into multiple two-hop subsystems, we develop closed-form expressions for bit error rate (BER) in flat Rayleigh fading channels. Our results are given as both lower bound and asymptotic expression based on an accurate upper bound of the end-to-end signal-to-noise ratio (SNR). It is shown that the proposed scheme has the same asymptotic BER performance and a much higher throughput compared with the conventional bidirectional relay scheme based on four transmission phases. Therefore, the proposed scheme is efficient for practical wireless applications. Simulation results are provided to validate the analysis.

Bit error rate analysis of the scheduled TAS with MRC for CR-MIMO systems

This paper presents bit error rate (BER) analysis of wireless sensor networks (WSNs) consisting of sensor nodes based on an IEEE 802.15.4 RF transceiver. Closed-form expressions for BER are obtained for WSNs operating over AWGN, Rayleigh and Nakagami-m fading channels. For the purpose of analysis, we consider an IEEE 802.15.4 RF transceiver using direct sequence spread spectrum-offset quadrature phase shift keying (DSSS-OQPSK) modulation under 2.4 GHz frequency band in a WSN. Analytical expressions for BER are derived for a wireless link between sensor nodes that act as a transmitter unit and a base station without considering the effect of interferers in the wireless environment. Numerical results for BER are obtained by varying the IEEE 802.15.4 standard specific physical layer parameters, such as number of bits used to represent a Zigbee symbol, number of modulation levels used in an OQPSK modulator, and various values of Rayleigh and Nakagami-m fading parameters, denoted as $$\alpha $$ ? and $$m$$ m , respectively. Moreover, optimum values of physical layer parameters are identified for improved system performance. It is found that error performance analysis of WSN shows improvement when lower number of bits is used to represent a Zigbee symbol. Specifically, under a Rayleigh fading channel which reflects a real-time WSN environment, the network exhibits better performance only when it is operated at high SNR values, i.e., BER of order $$10^{-2}$$ 10 - 2 is achieved when SNR lies in the range 5---15 dB. Also, the effect of fading parameters on network performance shows that better results are obtained for higher values of $$\alpha $$ ? and $$m$$ m for Rayleigh and Nakagami-m fading channels, respectively.

Free-space optical (FSO) communication offers advantages such as high bandwidth and high transmission rates, making it suitable for 6G backhaul networks. However, FSO systems have drawbacks like sensitivity to fog, atmospheric turbulence, and pointing errors. Radio frequency (RF) links are incorporated to achieve more reliable and wider-range communication. RF links are susceptible to rain and have limited bandwidth but are not sensitive to fog or atmospheric turbulence. The complementary characteristics of RF and FSO systems make hybrid RF-FSO systems highly effective in mitigating environmental impairments. Reconfigurable intelligent surfaces (RISs) can also further extend the coverage and enhance the system bit error rate (BER) performance of RF-FSO. The state-of-the-art link selection schemes in RIS-assisted hybrid RF-FSO are normally based on channel state information (CSI). However, there is a chance that the CSI is inaccurate or even unavailable to the receiver. This paper investigates a hybrid RF-FSO communication system where CSI is unknown. In our system, the RF link is modeled using the Nakagami-m distribution, and the FSO link accounts for attenuation, Gamma-Gamma distributed turbulence, and pointing errors. The key concept of our system is the adoption of index modulation (IM) for link switching so that CSI is not needed at both transmitter and receiver, and we call it RIS-IM. Exact closed-form expressions for the signal-to-noise ratio (SNR) of the RIS-RF and RIS-FSO links are derived using multivariate Fox’s H-function without using central limit theorem, including the probability density function (PDF) and cumulative distribution function (CDF). We derive the closed-form expressions for the average BER (ABER) for RIS-IM using the SNR statistics. Furthermore, numerical analyses of RIS-IM are conducted. The numerical results of RIS-IM are given comparing with pure-IM, RIS-FSO, and hard switching as benchmarks. Mont-Carlo simulation results demonstrate the superiority of RIS-IM in terms of ABER. In the future, more analysis including outage probability (OP) and ergodic capacity (EC) await further explorations.

Multiple-input multiple-output (MIMO) systems employing both maximal-ratio transmission and receive antenna selection (MRT&RAS) are studied in this paper. The examination has been done for independent and identically distributed (i.i.d.) flat Nakagami-m fading channels. Exact bit error rate (BER) expressions for binary phase shift keying (BPSK), differential binary phase shift keying (DBPSK) and binary frequency shift keying (BFSK) signals are derived by using the moment generating function (MGF)-based analysis method. By deriving upper bounds for exact BER expressions, it is shown that the investigated systems achieve full diversity orders at high signal-to-noise ratios (SNRs). Also, the ergodic system capacity and outage probability of MRT&RAS scheme have been analyzed. Exact BER results for different system and channel conditions are validated by Monte Carlo simulations.

In order to improve the bit error rate (BER) of multiple-input multiple-output orthogonal frequency diversity multiplexing (MIMO-OFDM) system in Nakagami-m channels, the model used rate-compatible punctured convolution (RCPC) and space-time block code (STBC) at the transmitter, maximum ratio combining (MRC) at the receiver was put forward. The signal-to-noise ratio (SNR) of the MIMO-OFDM system in Nakagami-m channels was studied, the expression of BER was given and the average BER upper limit after RCPC encode was further presented. Simulation result shows that the BER performance and the diversity gain of MIMO-OFDM with RCPC encoding achieve much improvement than the system with no RCPC. Owing to the free distance becomes shorter with the increase of code rate, the BER performance and the diversity gain of RCPC encoded MIMO-OFDM decreases a little

The bit error rate (BER) performance of the asynchronous uplink channel of multicarrier code division multiple access (MC-CDMA) systems with maximal ratio combining (MRC) is analyzed. The study takes into account the effects of channel path correlations in generalized frequency-selective fading channels. Closed-form BER expressions are developed for correlated Nakagami fading channels with arbitrary fading parameters. For channels with correlated Rician fading paths, the BER formula developed is in one-dimensional integration form with finite integration limits, which is also easy to evaluate. The accuracy of the derived BER formulas are verified by computer simulations. The derived BER formulas are also useful in terms of computing other system performance measures such as error floor and user capacity.

Channel coding is a fundamental procedure in wireless telecommunication systems and has a strong impact on the data transmission quality. This effect becomes more important when the transmission must be characterised by low latency and low bit error rate, as in the case of vehicle-to-everything (V2X) services. Thus, V2X services must use powerful and efficient coding schemes. In this paper, we thoroughly examine the performance of the most important channel coding schemes in V2X services. More specifically, the impact of use of 4th-Generation Long-Term Evolution (4G-LTE) turbo codes, 5th-Generation New Radio (5G-NR) polar codes and low-density parity-check codes (LDPC) in V2X communication systems is researched. For this purpose, we employ stochastic propagation models that simulate the cases of line of sight (LOS), non-line of sight (NLOS) and line of sight with vehicle blockage (NLOSv) communication. Different communication scenarios are investigated in urban and highway environments using the 3rd-Generation Partnership Project (3GPP) parameters for the stochastic models. Based on these propagation models, we investigate the performance of the communication channels in terms of bit error rate (BER) and frame error rate (FER) performance for different levels of signal to noise ratio (SNR) for all the aforementioned coding schemes and three small V2X-compatible data frames. Our analysis shows that turbo-based coding schemes have superior BER and FER performance than 5G coding schemes for the vast majority of the considered simulation scenarios. This fact, combined with the low-complexity requirements of turbo schemes for small data frames, makes them more suitable for small-frame 5G V2X services.