Simple half-duplex repetition-based relaying protocols can achieve spatial diversity at the expense of additional relaying signals in the time domain. In this paper, a linear unitary precoder based on a singular vector for cooperative systems with the amplify-and-forward (AF) relaying protocol is proposed in order to improve spectral efficiency. An exact expression of the precoder design is first derived for the case of equal power allocation. Then, water-filling power allocation is used in conjunction with the precoder to further increase the system capacity, where the precoder matrix is generated with an iterative process. From the implementation point of view, the channel state information (CSI) has to be estimated and quantized in systems, the detail of which is described in the sequel. The adaptive modulation and coding (AMC) technique with the proposed precoder is also discussed to achieve high throughput performance. Finally, numerical and simulation results are presented to demonstrate the effectiveness of the proposed technique in improving capacity and throughput.

In this letter, a circulation-based distributed space time trellis code (DSTTC) technique for amplify-and-forward (AF) relaying is proposed. The proposed circulation technique is a method of configuring new protocols from the existing protocols of which the performance is dependent on specific source to relay links. The simulation results show that the newly developed protocol is less dependent on weak conditions of specific links and a performance gain in frame error rate (FER) can be obtained over the original protocol.

Performance analysis of a dual-hop semi-blind amplify-and-forward (AF) relay system in mixed Nakagami-m and Rician fading channels, is proposed. We derived the closed-form expression for the cumulative distribution function (CDF) of the equivalent end-to-end signal to noise ratio (SNR), based on which the exact outage probability and symbol error probability (SEP) are investigated. The theoretical analysis is validated by Monte Carlo simulation results.

In this letter, a dual-hop wireless communication network with opportunistic amplify and forward (O-AF) relay is investigated over independent and non-identically distributed Nakagami-m fading channels. Employing Maclaurin series expansion around zero to derive the approximate probability density function of the normalized instantaneous signal-to-noise ratio (SNR), the asymptotic symbol error rate (SER) and outage probability expressions are presented. Simulation results indicate that the derived expressions well match the results of Monte-Carlo simulations at medium and high SNR regions. By comparing the O-AF with all AF relaying analyzed previously, it can be concluded that the former has significantly better performance than the latter in many cases.

We perform error probability analysis of the uncoded OFDM fixed gain Amplify-and-Forward (AF) relaying system with subcarrier permutation (SCP). Two SCP schemes, named: the best-to-best SCP (BTB SCP) and the best-to-worst SCP (BTW SCP) are considered. Closed-form expressions for the bit error rate (BER) of the above SCP methods are derived. Numerical results manifest that these SCP schemes may outperform one another, depending on the average channel conditions of the links involved. That is, BTB SCP is better at low signal-to-noise ratio (SNR) values, while BTW SCP prevails in the medium and high SNR regime. Thus, it could be concluded that OFDM AF relaying systems may switch from the BTB SCP to BTW SCP in order to achieve optimum BER performance. Moreover, using the derived end-to-end SNR probability density functions (PDF), tight upper bounds for the ergodic capacities of both SCP schemes are obtained.

We propose an incremental relaying protocol in conjunction with partial relay selection with the aim of making efficient use of the degrees of freedom of the channels as well as improving the performance of dual hop relaying with partial relay selection (DRPRS). Specifically, whenever the direct link from the source to the destination is not favorable to decoding, the destination will request the help of the opportunistic relay providing highest SNR of the links from the source. Theoretical analyses, as well as simulation results, verify that our scheme outperforms the DRPRS scheme in terms of bit error probability.

Selection relaying is a promising technique for practical implementation of cooperative systems with multiple relay nodes. However, to select the best relay, global channel knowledge is required at the selecting entity, which may result in considerable signaling overhead. In this paper, we consider the relay selection problem in dual-hop amplify-and-forward (AF) communication systems with partial channel state information (CSI). Relay selection strategies aiming at minimizing either the outage probability or the bit error rate (BER) with quantized CSI available are presented. We also propose a target rate based quantizer to efficiently partition the SNR range for outage minimized relay selection, and a target BER based quantizer for BER minimized relay selection. Simulation results show that near optimal performance is achievable with a few bits feedback to the selecting entity.

In this letter, we analyze the error performance of a code combining based cooperative diversity protocol. For coded transmission schemes, code-combining can obtain a near optimal low rate code by combining repeated codewords. An analytical method for evaluating the performances of such scheme is presented. We develop a closed form expression for pairwise error probability and tight upper bounds for bit error rate (BER) and frame error rate (FER) under Rayleigh fading environment. The analytical upper bounds are verified with simulation results.

In this paper, we study the performance of dual hop relaying in which the best relay selected by partial relay selection will help the source-destination link to overcome the channel impairment. Specifically, closed-form expressions for outage probability, symbol error probability and achievable diversity gain are derived using the statistical characteristic of the signal-to-noise ratio. Numerical investigation shows that the system achieves diversity of two regardless of relay number and also confirms the correctness of the analytical results. Furthermore, the performance loss due to partial relay selection is investigated.

The performance of two-way amplify-and-forward (AF) relay networks is presented. In particular, we derive exact closed-form expressions for symbol error rate (SER), average sum-rate, and outage probability of two-way AF relay systems in independent but not identically distributed (i.n.i.d.) Rayleigh fading channels. Our analysis is validated by a comparison against the results of Monte-Carlo simulations.

In this letter, power allocation methods are devised for Amplify-and-Forward (AF) opportunistic relaying systems aiming at minimizing the outage probability. First, we extend the result on outage probability in and develop an approximate expression to simplify the power allocation problem. A corresponding optimization problem is constructed and proved to be convex. Then an iterative numerical method is proposed to find the optimal power allocation factor. We also propose a near-optimal method which can directly calculate the power allocation factor to reduce computational complexity. Numerical results show that the proposed methods have a similar performance with the ideal one, and outperform equal power allocation significantly with little overhead.

In this letter, we present a closed-form bound of the average bit error rate (BER) performance for the multi-hop amplify-and-forward (AF) relaying systems with fixed gain in Rayleigh fading channel. The proposed bound is derived from the probability density function (PDF) of the overall multi-hop relay channel under the assumption of asymptotic high signal-to-noise ratio (SNR) at every intermediate relays. When intermediate relays actually operate at finite SNR, the proposed BER bound becomes looser as the SNR of the last hop increases. In order to reflect the effect of all the noise variances of relay links to the BER evaluation, a hop-indexed recursive BER approximation is proposed, in which the proposed bound of BER under asymptotic high SNR is used. The simulation results manifest that the proposed hop-indexed recursive BER approximation can not only guarantee accuracy regardless of the SNR of the last hop but also provide higher accuracy than the previous works.

In this paper, we consider an amplify-and-forward (AF) relay network where a source node transmits information to a destination node through the cooperation of multiple relay nodes. It is shown in prior works that the outage behavior and average throughput of the selection AF (S-AF) scheme where only the best relay node is chosen to assist can outperform the conventional all-participate AF (AP-AF) scheme. Assuming multiple antennas at the destination node and single antennas at other nodes in this paper, we propose a relay selection scheme according to the criterion of maximizing receive signal to noise ratio (SNR), where a group of relays is chosen to assist in the transmission simultaneously in a manner similar to cyclic delay diversity (CDD). Compared with S-AF, the proposed scheme achieves better outage behavior and average throughput. It can be seen from simulation results that the performance improvement of symbol error rate (SER) is significant compared with S-AF.

In this paper, we consider a dual-hop wireless cooperative network with amplify-and-forward (AF) relaying. The output signal-to-noise ratio (SNR) at the destination of the AF cooperative networks is in the form of the sum of harmonic mean of the source-relay channel SNR and the relay-destination channel SNR. Instead of deriving the exact probability density function (PDF) of the output SNR, we study the series expansion of this PDF around zero. This result is then applied to evaluate the performance of the AF cooperative systems over Nakagami-m fading channels, and closed-form high-SNR approximations of the average symbol error rate (SER) and the outage probability are derived. Next, we investigate the optimal power allocation (OPA) among the source node and the relays to minimize the approximate SER as well as the outage probability. It is shown that the optimal power allocation depends on the channel m parameters and the ratio of the source-relay channel gain to the relay-destination gain. In addition to the optimal power allocation, we also propose a low complexity sub-optimal power allocation (SubOPA) scheme. The performance improvement with optimal and sub-optimal power allocation is analyzed and validated by numeric results. It is shown that equal power allocation is near optimal when the relays are close to the source, while significant performance improvement is observed by both the optimal and sub-optimal power allocation schemes when the relays are close to the destination.

In this letter, a novel power allocation scheme is proposed to improve the outage performance of an amplify-and-forward (AF) cooperative communication network with multiple potential relays under the assumption that only mean channel gains are available at the transmitters. In this scheme, power allocation is studied jointly with a relay selection algorithm which has low computational complexity. Simulation results demonstrate the performance improvement of the proposed scheme in terms of outage behavior.

This letter studies the asymptotic bit error rate (BER) performance of multihop communication systems with amplify-and-forward relaying over Nakagami-m fading channels. Since it is difficult to find the exact probability density function (PDF) of the output signal-to-noise ratio (SNR) at the destination, we resort to the series expansion of this PDF in the neighborhood of zero. Building upon this result, a closed-form expression for the average BER in the high SNR region is derived. Numeric results show that the derived asymptotic BER expression is accurate at medium and high SNR for both independent identically distributed (i.i.d.) and independent non-identically distributed (i.n.i.d.) channels.

This paper studies a dual-hop amplify-and-forward (AF) relaying systems over shadowed Nakagami-m fading channels and derives an approximate analytical expression for the outage probability. The numerical results show that the derived analytical expression can provide very well approximations to the simulation results.

Combining relaying and multi-input multi-output (MIMO) transmission is a generic way to overcome the channel-fading impairments. Best antenna selection is a simple but efficient MIMO method that achieves the full diversity and also serves as a lower bound reference of MIMO performance. For a dual-hop MIMO system with an ideal amplify-and-forward (AF) relaying gain and best antenna selection, we provide a probability density function (PDF) of received signal-to-noise ratio (SNR) and an analytic BER equation when using M-ary PSK in Rayleigh fading channels. The analytic result is shown to exactly match with simulated one. Furthermore, the effect of link unbalance between the first hop and the second hop, due to differences in the number of antennas deployed in both hops as well as in the average power of channel coefficients, on the BER performance is numerically investigated and the results show that the links with better balance give better performance.

Prior studies have shown that the performance of amplify-and-forward (AF) relay systems can be considerably improved by using multiple antennas and low complexity linear processing at the relay nodes. However, there is still a lack of performance analysis for the cases where the processing is based on limited feedback (LFB). Motivated by this, we derive the closed-form expression of the outage probability of AF relay systems with LFB beamforming in this letter. Simulation results are also provided to confirm the analytical studies.

Cooperative communication enables single antenna to realize a virtual multiple antenna by sharing their antennas. Therefore, it offers transmit diversity. In this letter, we apply pre-coding scheme to the transmit symbols. Although pre-coding has shortcomings, it is possible to employ Space-Time Block Codes (STBC) with single antenna and achieve high gain.