The centralized training with decentralized execution (CTDE) paradigm has achieved strong performance in multi-agent reinforcement learning (MARL), yet on-policy actor–critic methods such as MAPPO can still exhibit training instability and late-stage performance collapse on coordination-intensive tasks. We address this issue with Self-Distillation MAPPO (SD-MAPPO), which maintains an Exponential Moving Average (EMA) teacher policy and regularizes the current actor with a KL-based temporal consistency term. Rather than correcting the underlying critic estimates, the proposed mechanism provides a slowly evolving policy reference. From a local analytical perspective, the EMA teacher bounds teacher–student drift over time, while the KL penalty locally damps abrupt policy fluctuations induced by noisy learning signals. Empirically, we evaluate on challenging SMAClite micromanagement tasks and complement win rate with test return, final-stage statistics, and late-stage update diagnostics. Across the primary four-task suite, SD-MAPPO improves final-stage robustness on the more collapse-prone maps while remaining broadly competitive on the easier tasks, with especially clear gains on 3s5z_vs_3s6z and 10m_vs_11m . Diagnostic analyses further show that the method consistently reduces late-stage policy-shift indicators such as old–new KL and clipping activation, even when critic-side changes are only mild. Overall, the results support SD-MAPPO as a lightweight actor-side stabilizer for instability-prone on-policy CTDE training rather than a universal improvement module. The method is plug-and-play, preserves decentralized execution, and adds only a small constant-factor training-time overhead. At deployment, action selection remains in the same actor-only regime as MAPPO because the EMA teacher is not used.

With the development of in-orbit satellite hardware technology, distributed model training and updating for in-orbit satellites has become a promising trend. However, performance significantly degrades due to heterogeneous data distribution and the lack of high-quality labeled data across satellites. To address these issues, we propose a distributed unsupervised representation learning method called Progressive Uniformity (DURL-PU) from a deep clustering perspective. DURL-PU explores instance-level, cluster-level, and structure-level representations to progressively enhance uniformity, thereby mitigating dimensional collapse caused by data heterogeneity. Specifically, we first perform instance-level contrastive learning to distinguish between positive and negative samples. Second, we introduce a cluster-level loss to improve within-cluster compactness and between-cluster dispersion while incorporating high-level semantic information. Finally, we propose a deep clustering-based structural loss to enhance the consistency of parameter distribution among different satellites. Extensive experiments under various heterogeneous data scenarios demonstrate the effectiveness of DURL-PU.

Prevalent dynamic network methods must provide additional task-IDs during inference with respect to class incremental learning. Otherwise, the classification accuracy will be significantly reduced. To tackle this issue, this work proposes a novel Class Incremental Learning with Forward Memory (CIL-FM) algorithm based on multi-head networks. The method learns and stores previously learned knowledge by introducing a forward branch, which then applies to new branches learning. A series of experiments confirm that forward branching can significantly improve the performance of dynamic network structures without task-IDs during inference. CIL-FM performs similarly to static network structures but excels in its continuous expansion as dynamic network structures without relying on task labeling cues in the inference phase. CIL-FM has better learning potential than static network structures.

Ensuring operator safety in collaborative workspaces with robots presents significant challenges within the Industry 5.0 landscape. Advanced algorithms play a crucial role in processing data from robotic workcells, enhancing operator monitoring accuracy while upholding privacy and ownership standards in industrial networks. This paper introduces a novel privacy-preserving approach for operator monitoring, leveraging edge-based federated learning (FL) and passive localization techniques. Our proposed localization system also accounts for the diverse execution time-cycles of robots in workcells, enabling evaluation of operator localization accuracy across different levels of robot productivity in various configurations. We validate the effectiveness of our approach through extensive experimental activities in robotic workcells equipped with radar sensors. Our evaluation considers diverse and realistic scenarios where training data is collected over heterogeneous time periods, representing robotic cells with varying characteristics and involving different operators. The results affirm the efficacy of the FL approach, particularly when utilizing heterogeneous datasets sourced from industrial robotic cells.

Abstract Codes that possess combination property (CP) and zigzag decoding (ZD) simultaneously (CP‐ZD) has broad application into edge aided distributed systems, including distributed storage, coded distributed computing (CDC), and CDC‐structured distributed training. Existing CP‐ZD code designs are based on scalar code, where one node stores exactly one encoded packet. The drawback is that the induced overhead is high. In order to significantly reduce the overhead, vector CP‐ZD codes are designed, where vector means the number of stored encoded packets in one node is extended from one to multiple. More specifically, in detailed code construction, cyclic shift is proposed, and the shifts are carefully designed for cases that each node stores two, three, and four packets, respectively. Comparisons show that the overhead is reduced significantly.

With the development of convolutional neural network (CNN), significant progress has been achieved in remote sensing image scene classification (RSISC). However, wide spatial range changes, complex scenes, as well as the high similarity between various classes and the significant difference in the same class, make it difficult to classify remote sensing images scenes. In this work, targetted at using finite remote sensing images to learn sufficient distinguishing features in a contrastive manner, we propose a novel multi-granularity and multi-scale progressive contrastive learning neural network (MMPC-Net). More specifically, we construct an end-to-end CNN model to mine discriminative features from multi-scale and multi-granularity representations. Afterwards, the discriminative knowledge between different features is summarized by introducing a progressive contrastive learning module, which can learn meaningful feature linking subtle changes in positive and negative pairs from massive samples. Experimental results over three widely-used benchmark datasets demonstrate that our methods can achieve comparative performance.

By separating huge dimensional matrix-matrix multiplication at a single computing node into parallel small matrix multiplications (with appropriate encoding) at parallel worker nodes, coded distributed computing (CDC) tackles the straggler problem and hence speeds up the computation significantly. Existing CDC encoding schemes are based on linear combination (LC), which have two drawbacks: First, heavy computational burden is introduced to both encoding and decoding phases. Second, large numerical error occurs in the decoding phase. To relieve these two effects, a fresh new 2D-SAZD-CDC framework that non-trivially generalizes 1D-SAZD-CDC is proposed, where D is short for dimension, the operation for encoding and decoding is implemented by shift-and-add (SA) and zigzag decoding (ZD) that replaces LC and matrix inversion, respectively. The non-trivial generalization lies in joint design of the operations in 2D are needed in both the encoding and the decoding phases, so as to ensure possesion of combination property (CP) and ZD from 2D viewpoint. More specifically, 2D-SA encoding is designed, 2D-ZD decoding (alternates intermittently between 2D) is proposed, and a proof for satisfying CP and ZD from 2D viewpoint is also given. Numerical studies show that 2D-SAZD-CDC significantly improves the numerical stability and computational load performance over existing LC based schemes.

Abstract Private information retrieval (PIR) means a user retrieves a file while revealing no information on which file is being retrieved. In classic PIR, the user needs to wait for the responses of all the storage nodes. However, in general, there may be some nodes that are unresponsive, in which case it is formulated as v ‐robust PIR in the network coding (NC) structured distributed storage system (DSS), where v denotes the number of unresponsive nodes. We consider PIR with unresponsive nodes under the framework of NC structured DSS. In particular, the storage nodes adopt combination property with zigzag decodable (CP‐ZD) storage code since it has the advantage of extremely low decoding complexity, which is promised by zigzag decoding (ZD) within a binary field. We design a v ‐robust PIR scheme with its download communication cost slightly larger than existing studies, but its decoding complexity is significantly reduced when compared with existing studies.

Linear combination (LC) based coded distributed computing (CDC) suffers from the problem of poor numerical stability. Therefore, LC-CDC based model parallel (MP) training for a deep nueral network (DNN) may have poor accuracy. To enhance accuracy, we propose to replace LC by shift-and-addition (SA) and replace matrix inversion by zigzag decoding (ZD) in the encoding and decoding process of each layer, respectively, and call the scheme Naive SAZD-CDC based MP training (N-SAZD-CDC-MP-T). However, N-SAZD-CDC-MP-T encounters the problem of bottleneck at the master node, which is caused by frequent encoding/decoding at the master node and frequent huge volume of data delivery between master and worker node. This bottleneck problem may pull down the training speed significantly. To alleviate this bottleneck problem, we further design an enhanced version, by offloading certain processing from master node to distributed encoding and updating (DEU) at the worker nodes and call it DEU-SAZD-CDC-MP-T. A proof that DEU-SAZD-CDC-MP-T automatically maitains the code structure during each iteration is provided. Extensive numerical studies show that the prediction accuracy of SAZD-CDC-MP-T improves significantly over that of Poly (which is representative of LC) based scheme. In addition, the training speed of DEU-SAZD-CDC-MP-T over N-SAZD-CDC-MP-T is improved significantly.

The coupling of unmanned aerial vehicle (UAV) and Internet of Things (IoT) systems can provide an efficient method to collect ground data for the Sixth Generation (6G) networks. Under this UAV-IoT scenario, an intelligent energy balancing strategy should be designed to achieve tunable energy fairness level among all the IoT devices, such that sensors can differ in their lifespans to meet specific application requirements. In this paper, we propose an intelligent $\alpha-$fairness strategy to balance the energy consumption among IoT sensors. Specifically, the heterogeneities among the sensor nodes, i.e., different data loads, diverse residual energy levels, and distinct channel gains, have been taken into consideration. Based on this, an $\alpha-$utility function is designed. In the maximization of the utility function, the bandwidth allocation, transmission power, and the UAV’s trajectory are jointly optimized. In addition, we also demonstrate how to judiciously tune the $\alpha$ value according to the specific application scenarios, thus to achieve different levels of energy fairness and promote the functional longevity of the system to the best effort.

Abstract Network densification is recognized as the key technology to meet the ever growing demand of data traffic in next generation wireless networks. However the proliferation of small cell base stations (SCBSs) introduces vulnerabilities to information security, as they are prone to eavesdropping attacks. In this paper, it is studied how user association strategies can be specifically tailored to meet this security challenge in a ultra dense heterogeneous cellular network(UDHCN) with a group of colluding eavesdroppers. In particular, the situation is considered where eavesdroppers may have limited capabilities in intercepting and decoding data traffic. In this setting each eavesdropper has to make its own decision on eavesdropping targets, and they are able to take concerted actions to sabotage information security. To address this challenge, a zero sum game framework to reflect the conflicting interests of users and eavesdroppers is proposed and a user association scheme is devised that aims to maximize system sum secrecy rate against these adversaries whose actions intend to minimize sum secrecy rate. The case that all adversaries have limited eavesdropping capabilities is first considered, and it is shown that the corresponding zero sum game is indeed a bilinear game, and its Nash equilibrium solution can be readily approximated using a saddle point Frank Wolfe(SP‐FW)algorithm. Then the framework is extended to the case where adversaries with a diverse configuration of eavesdropping capabilities exist. In this case, it is shown that the underlying minimax optimization problem is indeed a nonsmooth convex‐nonconcave one. A two stage method is proposed by first smoothing the objective function with a Hermite cubic polynomial approximation, and then obtaining a nearly stationary solution via a recently proposed proximal point gradient descent method. Simulation results show that the proposed framework leads to significant increases in sum secrecy rate and secrecy probability against both the capability‐limited adversaries and a hybrid type of adversaries.

The rise of Internet of Things (IoT) systems has enabled us to access real-time information about our surrounding environments. However, IoT data collection in hostile and inaccessible areas without infrastructure supports is a challenging issue due to the inherent physical constraints associated with the tiny sensors. A viable solution to this problem is to use agile and controllable unmanned aerial vehicles (UAVs) to collect the ground data and relay it to the remote cloud for further processing. Under this UAV–IoT scenario, the limited battery supply carried by the sensor must be efficiently utilized so as to prolong the lifetime of the IoT system. Nevertheless, lifetime extension does not merely entail the reduction of the sum energy expenditure of sensors. In this article, we first show that minimizing the sum energy consumption cannot effectively extend the system lifetime due to the imbalance in energy expenditure among sensors, which, in fact, can render early energy depletion for some overburdened sensors. We also reveal a tradeoff between energy efficiency and energy fairness. To tackle this imbalance issue, we then propose an$\alpha $-fairness approach to balance the energy consumption among IoT sensors. Specifically, in our study, the heterogeneities among the sensor nodes—different data loads, diverse residual energy levels, and distinct channel gains, have been taken into consideration. Based on this, an$\alpha $-utility function is designed. In the maximization of the utility function, the bandwidth allocation, transmission power, and the UAV’s trajectory are jointly optimized. In addition, we also demonstrate how to properly set the$\alpha $value according to the specific application scenarios, thus to achieve different levels of energy fairness and promote the functional longevity of the system to the best effort.

Abstract Cognitive radio based cooperative spectrum sensing (CSS) is severely affected when some secondary users maliciously attack it. Two attacks regarded as key adversaries to the success of CSS are spectrum sensing data falsification (SSDF) and primary user emulation attack (PUEA). Defending SSDF and PUEAs has received significant attention in research in the past decade globally. This paper performs a state‐of‐the‐art comprehensive survey of the researches on defending SSDF and PUEAs. First, the preliminaries like Hypothesis testing for detecting the primary user and different models of CSS are discussed briefly. Then a categorization of the defence mechanisms for defending both the attacks has been proposed as active and passive. Active mechanisms are suitable for an immediate defence in a limited time span, while passive mechanisms are suitable for flexible CSS systems that are ready to detect the attacks over a period of time and suppress them permanently by bringing changes in their underlying operations. An in‐depth tutorial on both the defence mechanisms is provided from the perspectives of the secondary users throughput and the interference to the primary user. Finally, a detailed survey on the open research problems in this area and some possible solutions has been performed.

In edge computing applications, data is distributed across several nodes. Failed nodes mean losing part of the data which may hamper edge computing. Node repair is needed for frequent nodes failure in edge computing systems. Codes with both the combination property (CP) and Binary Zigzag Decodable (BZD) are referred to as CP-BZD codes. In this paper, without adding extra checking bits, new coding constructions of CP-BZD codes are proposed to repair the failed node in distributed storage systems. All constructed codes can be decoded by the zigzag-decoding algorithm. Numerical analysis shows that compared with the original CP-BZD codes, our proposed schemes obtain better repair efficiency.

Coded distributed computing (CDC) can overcome the problem that the computation of matrix multiplication with an extremely huge dimension cannot be executed in a single Internet-of-Things (IoT) node. All the encoding of existing CDC schemes are based on the linear combination (LC) to generate independent computation tasks, which introduces a heavy computational load, including a significant volume of expensive multiplications (compared with inexpensive additions) and even more expensive divisions to the encoding and decoding phases. Note that the number of elementwise multiplications of the LC operation during the encoding phase is N times that of the original computation task, where N denotes the number of worker nodes. In this article, to avoid expensive multiplications introduced by LC, a fresh new CDC framework based on shift-and-addition (SA) over the real field is proposed. In addition, to avoid the expensive matrix inverse operation (divisions) in the decoding phase, zigzag decoding (ZD) is incorporated. The proposed scheme, which combines SA and ZD and is hence named SAZD-based CDC, avoids expensive multiplications and divisions in both the encoding and decoding phases. It targets the following simultaneous objectives: an arbitrary K out of N generated computation tasks is independent and can recover the original computation tasks with the ZD algorithm, and the shift distance is small so as to cause a light additional computational load in the computation phase. Both analysis and practical study show that compared to the LC-based CDC, the SAZD-based CDC significantly reduces the computational load.

This paper is concerned with the dynamics of spatially-coupled low-density parity-check (SC-LDPC) ensembles for transmission on general binary memoryless symmetric (BMS) channels under belief-propagation (BP) decoding. The decoding waves of such ensembles are found to exhibit solitonic behavior, propagating along the Tanner graphs at asymptotically constant velocities. A low-complexity approach termed interpolated density evolution (IDE) is proposed to predict the decoding wave velocities. In this approach, the densities of a decoding wave are approximated by interpolating between some fixed points of an uncoupled DE recursion with one-dimensional functions. Two transfer functions for updating these interpolation functions in the IDE recursion are established and a simple strategy is introduced to deal with the coexistence of multiple transition regions. In addition, a threshold analysis is developed based on two ansatzes, explaining why our approach can achieve a good trade-off between computational cost and accuracy, as illustrated with some numerical examples at the end of this paper.

For one moving Internet of Things (IoT) collector to download files from nearby industrial IoT devices, storing network coded files into multiple IoT devices can achieve good reliability performance if the following (n, k) erasure property (EP) is fulfilled: k source packets are encoded into n packets, and k packets chosen from these n packets in an arbitrary manner can reconstruct all the source packets. Besides, low decoding complexity is desired for time-sensitive applications and energy-limited moving IoT collectors, and binary zigzag decoding (BZD) achieves significantly low decoding complexity. The objective of previous EP-BZD designs is unilateral, which limits its application scenarios. In this article, a novel EP-BZD code is designed, which achieves good tradeoff among largest storage room overhead (SRO), SRO variance, and wide range of (n, k). To implement such a code, the source packets are shifted by several bits, respectively, and then Xored together. The numbers of bits shifted are represented by a matrix, which is obtained from a specially constructed triangle by taking a certain maximal submatrix. The triangle is obtained by a series of steps, including the construction of base vector, parallelogram, trapezoid, etc. The proof that the proposed code possesses EP and BZD simultaneously is also provided. A series of comparisons verify that the proposed code achieves significantly better tradeoff among triple objectives than existing EP-BZD codes.

In drive-thru internet, road side units (RSUs) are deployed along the road, which facilitate content dissemination to the vehicles on the go through vehicle to infrastructure (V2I) communications. Due to many factors including short and intermittent connections, the fading nature of wireless channel, and relatively fast speed of the vehicle, the vehicles might not be able to receive the complete content file successfully. Therefore, caching a file at multiple RSUs along the road in a collaborative manner is needed. To this end, the combination property (CP) is desired for caching the content: if k source packets are mapped into n ≥ k packets and with any k out of these n packets are able to recover all the information. Reed-Solomon (RS) codes possess CP and have been widely adopted in distributed storage (DS) systems. RS codes operating within a large size finite field have high encoding/decoding complexity, which dramatically increase the computation burden and prolong the processing delay. By introducing several overhead bits and by smart design, binary zigzag decoding (BZD) can significantly reduce the decoding complexity, and CP-BZD codes that possess both CP and BZD have been proposed recently. For CP-BZD structured drive-thru internet system, packets delivered over the air might encounter errors in certain bits. In this work, without adding extra checking bits, existing overhead bits in CP-BZD is used instead, and a novel decoding method that reaps error correction ability is proposed. In other words, our method has self-error correction ability. Complexity analysis of this proposed method is performed and a low complexity algorithm is designed. This error correction module is completely optional, adaptable, and flexible to be deployed to various environments. Numerical studies show that the proposed method can achieve CP with both low decoding complexity and self-error correction.

The proliferation of Internet of Things (IoT) systems provides us a formidable way to monitor a multitude of things by recording field data and delivering it to the faraway controlling center. However, in hostile or inaccessible areas without infrastructure supports, transmission of IoT data is a daunting task due to the limited physical constraints associated with the weak communication unit and tiny battery supply at the ground sensors. A feasible solution to this problem is to use flexible and programmable unmanned aerial vehicles (UAVs) to gather the ground IoT data and then relay it to the end user, forming a UAV-IoT data collection system. Nevertheless, as we reveal in this article, there is a tradeoff between the two performance metrics-system throughput and sensor energy efficiency. Therefore, the data collection for UAV-IoT system should be power-aware, i.e., expending just enough energy to achieve the required system performance. To this end, in this article, by locating the optimal system parameters-the UAV flying speed and altitude, as well as the frame length at the MAC layer, we can strike a balance between the two conflicting metrics, in that, we can maximize the energy efficiency at the ground sensors, while satisfying the required system performance at the same time. In addition, with a cross-layer design, we can adaptively tune the frame length at MAC layer according to the varying UAV flying speed at the PHY layer, thus promptly switching the system between “system-efficient mode” and “energy-efficient mode”.

A code is said to possess the combination property if k source packets are mapped into n k packets and any k out of these n packets are able to recover the information of the original k packets. While the class of maximum-distance-separable codes are well known to have this property, its decoding complexity is generally high. For this reason, a new class of codes which can be decoded by the zigzag-decoding algorithm is considered. It has a lower decoding complexity at the expense of extra storage overhead in each parity packet. In this work, a new construction of a zigzag decodable code is proposed. The novelty of this new construction lies in the careful selection of the amount of bit-shift of each source packet in obtaining each parity packet. Besides, an efficient on-the-air repair scheme based on physical-layer network coding is designed.

Two-hop security communication with an eavesdropper in wireless environment is a hot research direction. The basic idea is that the destination, simultaneously with the source, sends a jamming signal to interfere the eavesdropper near to or co-located with the relay. Similar as physical layer network coding, the friendly jamming signal will prevent the eavesdropper from detecting the useful information originated from the source and will not affect the destination on detecting the source information with the presence of the known jamming signal. However, existing investigations are confined to Gaussian distributed signals, which are seldom used in real systems. When finite constellation signals are applied, the behavior of the secrecy rate becomes very different. For example, the secrecy rate depends on phase difference between the input signals with finite constellations, which is not observed with Gaussian signals. In this paper, we investigate the secrecy capacity and derive its upper bound for the two-hop relay model, by assuming an eavesdropper near the relay and the widely used M-PSK modulation. With our upper bound, the best and worst phase differences in high SNR region are then given. Numerical studies verify our analysis and show that the derived upper bound is relatively tight.

A pair of terminals exchanging information via a layer of parallel relay nodes under slow fading is considered. Two protocols are proposed based on the combination of opportunistic relaying (OR) with analogue network coding (ANC), named ORANC, or with digital network coding (DNC), named ORDNC, respectively. Two schemes/versions of ORDNC, including 2‐phase ORDNC (2P‐ORDNC) and 3‐phase ORDNC (3P‐ORDNC) are proposed. Their outage performances are investigated. ORANC and 2P‐ORDNC are proved to achieve optimal diversity‐multiplexing tradeoff (DMT), whereas 3P‐ORDNC is proved to be suboptimal. However, from diversity viewpoint only, all the above schemes are proven to achieve full diversity order. Simulation results verify the analysis, and show that 3P‐ORDNC and ORANC shows advantage at low‐ and high‐data rate regions, respectively.

Index coding (IC), which can be regarded as a special class of network coding, deals with the problem of sending a number of packets to a group of receivers, each of which requests one packet and may have some other packets in its cache. This paper generalizes the IC problem in that both the packet requested by a receiver and the packets in its cache can be linear combinations of the packets. To minimize the number of transmissions required, a heuristic algorithm based on the idea of partitioning the users into coding groups is designed. To realize this idea, a polynomial time algorithm to determine whether a set of users form a coding group over the binary field or a field with a size larger than the number of users is constructed. For users that form a coding group, the corresponding encoding vector can be also found. A lower bound is derived in order to evaluate the performance of the heuristic algorithm. Numerical results show that the number of transmissions required by the heuristic algorithm and the lower bound both grow roughly linearly with the number of users, and the heuristic algorithm outperforms some benchmark algorithms.

The multiple access relay channel (MARC) where multiple users send independent information to a single destination aided by a single relay under large-scale path loss and slow fading is investigated. At the beginning, the users take turns to transmit their packets. The relay is not aware of the erasure status of each packet at the destination but has the knowledge of the average signal-to-noise-ratio (SNR) of every communication link. With this knowledge, the relay applies network coded retransmission on the overheard packets so as to maximize the expected total number of recovered packets or minimize the average packet loss rate at the destination. Several network coding (NC) strategies at the relay are designed. In particular, for the case where the relay is given only one time slot for retransmission, an optimal NC construction is derived. For the multiple-slot case, three sub-optimal schemes are investigated, namely network coding with maximum distance separable (MDS) code (NC-MDS), the worst-user-first (WUF) scheme and a hybrid of NC-MDS and WUF. We prove that NC-MDS and WUF are asymptotically optimal in the high and low SNR regimes, respectively. A lower bound on the average packet loss rate has been derived. Numerical studies show that, in a cellular system, the hybrid scheme offers significant performance gain over a number of existing schemes in a wide range of SNR. We also observe that performance curves of both WUF and the hybrid scheme touch the derived lower bound in the low SNR regime.

In the original index coding problem, each user has a set of uncoded packets as side information, and wants to decode some other packets from the source node. The source node aims at satisfying the demands of all users as quickly as possible. With linear network coding, this is accomplished by broadcasting linear combinations of the source packets over some finite field. Since the broadcast is performed over a wireless channel, a user may overhear some coded packets that are not intended to him/her. This motivates a generalization of the index coding problem to the case where linearly coded packets are used as side information. We show that this generalized linear index coding problem is equivalent to solving a system of multi-variable polynomial equations. A heuristic solution is constructed and is applied to the broadcast relay channel.

A single source-destination pair communicating via a layer of parallel relay nodes under quasi-static slow fading environment is investigated. One existing transmission protocol is considered, namely, the combination of the distributed version of the half symbol-rate complex constellation orthogonal space-time block codes (OSTBC) with adaptive amplify-and-forward (AAF) relaying strategy. We call this transmission protocol as distributed orthogonal space-time block coded adaptive amplify-and-forward (DOSTBC-AAF). To improve the performance of DOSTBC-AAF, a distributed on-off power control (OOPC) rule applied to the relays is analytically derived and is proved to achieve full diversity order. The outage performance of DOSTBC-AAF with and without power control is evaluated. Our simulation results show that DOSTBC-AAF with all relays transmitting at full power (FP) achieves no diversity gain, whereas DOSTBC-AAF with OOPC achieves full diversity order. Correspondingly, at high signal-to-noise ratio (SNR), the diversity-multiplexing tradeoff (DMT) achieved by DOSTBC-AAF (OOPC) is analytically derived and is numerically shown to outperform DOSTBC-AAF (FP) significantly.

The achievable outage probability of the diamond relay network under Rayleigh fading is investigated. Two existing transmission protocols are considered, namely, the Alamouti-Coded Amplify-and-Forward (ACAF) and the Alamouti-Coded Decode-and-Forward (ACDF). For ACAF, a distributed optimal power control rule for the two relays is analytically derived. Simulation results show that with this power control rule, the diversity gain of ACAF increases from one to two, and its performance approaches that of ACDF in the high signal-to-noise ratio (SNR) regime. For ACDF, a performance bound is analytically obtained: for any outage probability e, its SNR offset is bounded above by 3 dB and its e-outage rate is within 1 bit of the e-outage capacity of the diamond relay network.