Closed-form Symbol Error Rate Research Articles

On performance of cooperative network based on OFDM combined with TDM using MMSE-FDC in the presence of nonlinear HPA

In this paper, we analyze the impact of nonlinear high-power amplifier (HPA) on the performance of cooperative network based on orthogonal frequency division multiplexing combined with time-division multiplexing (OFDM/TDM) using minimum mean-square-error frequency-domain combining (MMSE-FDC) in a frequency-selective fading channel. We design a novel MMSE-FDC weights while taking into account the nonlinearity of HPA at source and relay. Closed-form symbol error rate and outage probability expressions are derived while approximating the residual inter-slot interference after the MMSE-FDC as a random Gaussian variable. We discuss and address the nonlinear OFDM/TDM system design issues in cooperative network using the obtained simulation and theoretical results. We show that the OFDM/TDM with MMSE-FDC can be used to reduce the impact of nonlinear HPA on overall performance of cooperative network in comparison to OFDM while providing the target quality-of-service for reduced required signal-to-noise ratio. This is because OFDM/TDM with MMSE-FDC achieves frequency diversity in addition to cooperative diversity, while reduced peak-to-average power ratio makes it more robust on nonlinear degradation due to HPA saturation in comparison to conventional OFDM.

Performance Analysis of Amplify and Forward Cooperative Relaying Protocol in Wireless Communication System

Cooperative relaying has been well appreciated to be a key concept of future wireless systems capable of yielding high network reliability and significant error rate reduction. However, in such paradigm of communication, the total limited power may be wasted without providing minimum performance requirements such as network lifetime if it is not well allocated between the cooperating nodes in an efficient way. In this work, we mainly address the problem of network lifetime limitation in wireless relay communication system by developing optimal power allocation techniques. In the communication scenario, a source sends information to a destination with the help of multiple relay nodes operating in amplify-and-forward relaying protocol. As a parameter of measurement, we particularly address the symbol error rate (SER) performance for MPSK signal using the concept of moment generating function. Due to the complexity of the closed-form SER expression, we then find a tight corresponding lower bound to show useful insights in terms of analysis. Next, we develop a cooperation strategy where only a best relay that maximizes the end-to-end signal-to-noise ratio assists the transmission to further improve the performance of the previous system. In addition, numerical results are presented to validate the theoretical analysis.

Performance Analysis and Optimal Power Allocation for Space–Time and Amplify-and-Forward Cooperative System

In this paper, we consider a space–time and amplify-and-forward (ST-AF) cooperative system which consists of two-antenna source, single-antenna relay and destination. Source transmits Alamouti space–time coding symbols to destination with cooperation of relay which adopts AF strategy. Closed-form symbol error rate (SER) is derived for the ST-AF system with PSK signals. Moreover, a SER approximation is developed to show the asymptotic performance of the ST-AF cooperative system in medium and high SNR regimes. For comparison, the SER approximation of another cooperative space–time coding (C-STC) scheme is also derived. Theoretical analysis shows that the ST-AF can obtain more diversity gain and achieve higher diversity order than C-STC. Statistical optimal power allocation (OPA) algorithm for the ST-AF cooperative system is presented based on the SER performance. It turns out the OPA only depends on the channel links related to the relay, not depend on the direct link between source and destination. Finally, numerical simulations validate the theoretical analysis.

Performance analysis of dual-hop fixed-gain AF relaying systems with OSTBC over Nakagami-m fading channels

In this paper, we present outage probability and symbol error rate (SER) performance analyses of a dual-hop transmission using fixed-gain amplify-and-forward relaying in flat Nakagami-m fading channels. The system under consideration is equipped with multiple antennas at source and destination adopting orthogonal space-time block coding to provide transmit diversity and maximum ratio combining to provide receive diversity, respectively. For integer and half-integer m values, closed forms of exact outage probability and moment generating function (MGF) expressions are derived through cumulative distribution function (CDF) of the overall system signal-to-noise ratio. Closed-form exact SER expressions based on the overall CDF are obtained for binary phase shift keying, binary frequency shift keying and M-ary pulse amplitude modulation. Exact SER expressions based on the MGF method are also obtained for binary differential phase shift keying, M-ary phase shift keying and M-ary quadrature amplitude modulation. Moreover, the asymptotic diversity order analysis is performed through derivations of asymptotic outage probability and SER. Theoretical analyses are validated by Monte Carlo simulations showing perfect match between each other.

Performance Analysis of Space-Time and Amplify-and-Forward Cooperative System

In this paper, we consider a space-time and amplify-and-forward(ST-AF) cooperative system which consists of two-antenna source, single-antenna relay and destination. Source transmits Alamouti space-time coding symbols to destination with cooperation of relay which adopts AF strategy. Closed-form symbol error rate(SER) is derived for the ST-AF system with PSK signals. Moreover, an SER approximation are developed to show the asymptotic performance of the ST-AF cooperative system in medium and high SNR regimes. For comparison, the SER approximation of another cooperative space-time coding(C-STC) scheme is also derived. Theoretical analysis shows that the ST-AF can obtain more diversity gain and achieve higher diversity order than C-STC. Finally, computer simulations validate the theoretical analysis.

Cooperative communication with imperfect channel information: Performance analysis and optimum power allocation

In this paper, symbol-error-rate (SER) performance analysis is provided for decode-and-forward (DF) and amplify-and-forward (AF) cooperation schemes in wireless networks with imperfect channel information. We derive closed-form SER formulations for a single relay system with square MQAM signals in a flat Rayleigh fading channel. Moreover, closed-form and high SNR tight SER approximations are established to show the asymptotic performance of the cooperation protocols. Simulations and comparisons verify that these approximations lead to similar results to those from the exact SER formulations for different power allocation methods. Furthermore, based on these SER performance analyses, we determine the optimum power allocation for the AF and DF cooperation scenarios.

Performance Analysis of Differential Modulation and Relay Selection with Detect-and-Forward Cooperative Relaying

This letter analyzes the performance of a multi-relay cooperative communication scheme with differential modulation and relay-selection (DM-RS). The scheme consists of a source, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> relays, and a destination, where the best relay is selected to forward the source node's signal with detect-and-forward (DetF) protocol. The capacity outage probability (COP) and symbol error rate (SER) of the scheme are investigated. In particular, a closed-form COP and an approximation at large signal-to-noise ratio (SNR) are derived. The COP approximation shows that the scheme can achieve a full diversity order of N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> +1. Furthermore, a closed-form SER approximation of the scheme with multiple phase shift keying (MPSK) modulation is derived. Simulation results confirm the presented mathematical analysis.

Peroformance analysis of decode-and-forward MIMO relay channels with OSTBCs

Performance analysis is presented for multiple-input multiple-output (MIMO) relay channels employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where the source and the destination are equipped with N s and N d antennas, and communicate with each other with the help of a multiple-antenna relay operating in decode-and-forward (DF) mode. Over independent, not necessarily identical Rayleigh fading channels, exact closed-form symbol error rate (SER) expressions are derived for various digital modulation formats for both the OSTBC transmission with and without the direct link. The moment generating functions (MGFs) for overall system signal-noise ratios (SNRs) are also derived, based on which we present a unified SER analysis. The analysis shows that full spatial diversity order can be achieved for the DF MIMO relay channel by adopting OSTBC transmissions and maximal ratio combining (MRC) receptions. All the analytical results are confirmed through comparison with the results obtained using Mento Carlo simulations.

Analytical performance evaluation of dual-hop cooperative communication under fading environments

This paper mainly investigates the performance of cooperative communication systems over dissimilar Nakagami-q (Hoyt) and Nakagami-m fading channels. Its relaying protocol selects these relays successfully regenerating the received signals to cooperatively forward the signals through orthogonal channels. The destination finally demodulates the messaged received in both phases exploiting Maximal-Ratio Combining (MRC) technique. Closed-form Symbol Error Rate (SER) expressions for repetition-based relaying protocol and space-time-code-based protocol are elaborated, respectively. Numerical result comparisons between the repetition-based protocol and the space-time-code-based protocol evidently indicate that, given the same spectral efficiency, the latter can provide better performance in terms of SER.

Symbol Error Rate Analysis and Power Allocation for Adaptive Relay Selection Schemes

In this paper, we analyse the symbol error rate (SER) performance of adaptive relay selection schemes (ARS) in a general dual-hop multiple-relay network. Specifically, we provide a closed-form SER expression for ARS which is tight over the whole signal-to-noise ratio (SNR) region. In addition, the derived SER can be readily extended to conventional relay selection schemes, i.e. amplify-and-forward relay selection (AF-RS), perfect decode-and-forward relay selection (PDF-RS), adaptive decode-and-forward relay selection (ADF-RS), and cooperative-maximum-ratio-combining decode-and-forward relay selection (CDF-RS). Transmit power allocation based on the simplified SER is presented to improve the system performance. The analytical results are verified by computer simulations.

Simple closed-form asymptotic symbol error rate of selection combining and its power loss compared to the maximal ratio combining over Nakagami m fading channels

This paper derives closed-form asymptotic symbol error rates (ASERs) for MPSK and MQAM signals with selection combining (SC) over Nakagami-m fading channels. It also presents a closed-form expression for the power loss of SC compared to maximal ratio combining (MRC) over a Nakagami- m fading channel. It is found that this power gap is a function of only the number (L) of independent Nakagami-m channels and the fading parameter m. For a fixed m, the gap monotonically increases with L. For a fixed L, the gap monotonically increases with m and approaches 10 log10 L dB (the asymptotic gap between MRC and SC in an AWGN channel) as m ? ?. In addition, numerical results show the accuracy of the ASERs obtained from closed-form expressions for both MRC and SC with MPSK and MQAM signals for large SNRs. They also show that the SNR gap is identical to that predicted by the analysis for arbitrary L and m.

Closed-form symbol error rate expression of decode-and-forward relaying using orthogonal space–time block coding

The authors investigate the symbol error rate (SER) performance of the cooperative decode-and-forward (DF) relaying strategy with orthogonal space–time block coding (OSTBC) applied at all links of source-relay, source-destination and relay-destination. Only when one relay node is able to correctly decode the OSTBC codeword of the source, it will forward source information to the destination with the same OSTBC codeword. The exact SER expressions of DF relaying with OSTBC are presented for M-PSK and M-QAM modulations, respectively, over dissimilar Rayleigh fading channels. By virtue of the multinomial theorem and the law of total probability, the derived expressions are further deduced in closed form. Simulations demonstrate the proposed closed-form analytical results. It is pointed out that such results have seldom appeared in literatures before.

Precise SER Analysis and Performance Results of OSTBC MIMO-OFDM Systems over Uncorrelated Nakagami-m Fading Channels

Although the topic of multiple-input multiple-output (MIMO) based orthogonal frequency division multiplexing (OFDM) over different fading channels is well investigated, its closed form symbol error rate (SER) expressions and performance results employing orthogonal space time block codes (OSTBCs) over uncorrelated frequency-selective Nakagami-m fading channels are still not available. The closed form expressions are extremely useful for evaluating system's performance without carrying out time consuming simulations. Similarly, the performance results are also quite beneficial for determining the system's performance in the sense that many practical wireless standards extensively employ MIMO-OFDM systems in conjunction with M-ary quadrature amplitude modulation (M-QAM) constellation. This paper thus, derives exact closed form expressions for the SER of M-ary Gray-coded one and two dimensional constellations when an OSTBC is employed and Nt transmit antennas are selected for transmission over frequency-selective Nakagami-m fading channels. For this purpose, first an exact closed-form of average SER expression of OSTBC based MIMO-OFDM system for M-ary phase shift keying (M-PSK) using traditional probability density function (PDF) approach is derived. We then compute exact closed form average SER expressions for M-ary pulse amplitude modulation (M-PAM) and M-QAM schemes by utilizing this generalized result. These expressions are valid over both frequency-flat and frequency-selective Nakagami-m fading MIMO channels and can easily be evaluated without using any numerical integration methods. We also show that average SER of MIMO-OFDM system using OSTBC in case of frequency-selective Rayleigh fading channels remains independent to the number of taps, L of that fading channel and the performance of the same system for two-tap un-correlated Rayleigh and Nakagami-m fading channels is better than that of the correlated one. Moreover, Monte Carlo simulation of MIMO-OFDM system using multiple transmit and receive antennas for different modulations is presented to validate our theoretical results. Finally, due to availability of closed form expressions, we further provide the performance results of MIMO-OFDM system over frequency-selective Nakagami-m fading channels employing (M-QAM) using OSTBCs under the transmission rate equal to 1, 2 and 3 bit(s)/s/Hz, respectively.

Performance Analysis of TDMA Relay Protocols Over Nakagami-$m$ Fading

Several time-division multiple-access (TDMA) cooperative wireless relay protocols and their performances have recently been developed by Nabar, Bolcskei, and Kneubuhler. Their work, however, is limited to an upper bound-based performance analysis for Rayleigh fading. We thus provide an exact analysis of two of their protocols in single-relay and multiple-relay networks over independent identically distributed (i.i.d.) Nakagami-m fading channels. Our analysis is focused on an Alamouti-coded system with two-stage protocols, fixed-gain amplify-and-forward (AF) relays, and maximal ratio combiner (MRC) reception. The performance metrics are the capacity, the diversity order, and the symbol error rate (SER). The closed-form moment-generating function (MGF) of the total end-to-end signal-to-noise ratio (SNR) is derived. The MGF is then used to derive the diversity order and the SER of M-ary phase-shift keying (M-PSK) and M-ary quadrature amplitude modulation (M -QAM). It is found that the end-to-end SNR for relaying with orthogonal channels is higher than that of nonorthogonal relay channels. The diversity order of a multiple-relay network (n relays) in a Nakagami-m environment is shown to be (n + 1)m. The closed-form SER expressions for relay-destination links with high SNRs and static relay-destination links are derived. Numerical and simulation results are provided to verify the analysis.

Performance Analysis of OSTBC Transmission in Amplify-and-Forward Cooperative Relay Networks

A performance analysis is presented for amplify-and-forward (AF) cooperative relay networks employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where multiple antennas are equipped at the transmitter. We develop a symbol-error-rate (SER) and outage performance analysis for OSTBC transmissions with and without cooperative diversity over flat Rayleigh fading channels. We first derive exact probability density functions (pdf's) and cumulative distribution functions (cdf's) for the system SNR without direct transmission with an arbitrary number of transmit antennas and then present the exact closed-form SER and outage probability expressions. Next, we derive the moment-generating function (MGF) for the overall system SNR with direct transmission and present the exact SER and outage probability with joint transmit antenna diversity and cooperative diversity. The theoretical analysis is validated by simulations, which indicate an exact match between them. The results also show how the transmit antenna diversity and the cooperative diversity affect the overall system performance.

Error Probability Analysis of Combining Space-Time Block Coding and Scheduling in MIMO Systems

In this paper, we investigate a joint diversity scheme combining space-time block coding (STBC) and opportunistic scheduling in a multiple-input multiple-output (MIMO) system. In this scheme, the user with the maximum effective signal-to-noise ratio (SNR) is adaptively selected, and the closed-form symbol error rate (SER) of the joint diversity scheme is presented. The exact SER of the joint diversity scheme can then be derived for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary QAM and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary PSK modulations in flat Rayleigh fading channels. Furthermore, using asymptotic analysis, we approximate the SER and clearly quantify both the diversity order and SNR gain for the joint diversity scheme. Based on this analysis, we show that the diversity order of the joint diversity scheme is improved in proportion to multiuser diversity (MUD) and spatial diversity, whereas the SNR gain worsens as spatial diversity increases. Finally, analytical results are verified through Monte-Carlo simulation results.

On relay selection for decode-and-forward relaying

In this letter, we consider a multi-relay network operating in decode-and-forward mode. We propose a novel relay selection method with a low implementation complexity. Unlike the competing schemes, it requires neither error detection methods at relay nodes nor feedback information at the source. We derive a closed-form symbol error rate (SER) expression for multi-relay network under consideration and demonstrate that the proposed selection method is able to extract the full diversity. Extensive Monte Carlo simulations are also presented to confirm the derived SER expressions and to compare the performance of the proposed scheme with its competitors.

Transceiver Design for Spatial Multiplexing Based on Prewhitening Detector

In this paper, we propose a joint-transmitter-and-receiver design for spatial multiplexing based on a novel prewhitening detector (PWD). By using decision feedback equalization (DFE), Gaussian approximation, a prewhitening filter, and a matched filter, the proposed PWD transforms the multiple-input-multiple-output (MIMO) system into several parallel single-input-single-output (SISO) schemes and facilitates single-symbol detection. The proposed scheme achieves near-optimal symbol recovery with a complexity similar to that of a minimum-mean-square-error decision feedback equalizer (MMSE-DFE). The closed-form symbol error rate (SER) of the PWD is derived, which can be used to closely predict the ML performance for uncoded V-BLAST schemes. By assuming full channel knowledge at the transmitter side, we use a preequalizer and a precoder in a downlink scenario. The preequalizer can transfer the feedback part of the DFE to the transmitter side and thus provide better performance in a low signal-to-noise ratio (SNR) with reduced receiver complexity. The precoder designed to minimize the SER of this system can further improve performance without affecting the complexity at the receiver side.

Symbol Error Rate of Cooperative Transmission Using OSTBC

We investigate the symbol error rate (SER) of the cooperative transmission with the decode-and-forward relay protocol under Rayleigh fading channels. The technique of orthogonal space-time block coding (OSTBC) is applied at the links source-relay, source-destination and relay-destination. A closed-form SER expression is derived. Simulation results demonstrate the theoretical solutions.

Capacity and SER Analysis of MIMO MRC Systems in an Interference-Limited Environment

The effect of co-channel interference (CCI) is considered in multiple-input multiple-output (MIMO) systems employing maximal ratio combining (MRC) under independent and identically distributed Rayleigh fading. Closed-form capacity and symbol error rate expressions are presented to evaluate the performance without any numerical integrations or statistical simulations. The analytical results are compared with Monte Carlo simulations and the good agreement is obtained.