A distributed belief propagation protocol is developed to carry inference and decoding tasks using wireless sensor networks with high-dimensional, correlated observations. Statistical dependencies are modeled using factor graphs. The overall a-posteriori probability is factored so that its factor graph representation can be mapped to the actual communication network. Sum-product message passing updates over the graphical model can thus be mapped to messages among sensors. As an application scenario, distributed spectrum sensing is considered. Simulated tests show that exploiting the correlation present among sensor observations can considerably improve sensing performance.

A network-compressive transmission protocol is developed in which correlated sensor observations belonging to a finite alphabet are linearly combined as they traverse the network on their way to a sink node. Statistical dependencies are modeled using factor graphs. The sum-product algorithm is run under different modeling assumptions to estimate the maximum a posteriori set of observations given the compressed measurements at the sink node. Error exponents are derived for cyclic and acyclic factor graphs using the method of types, showing that observations can be recovered with arbitrarily low probability of error as the network size grows. Simulated tests corroborate the theoretical claims.

Physical-layer network coding over wireless networks can provide considerable throughput gains with respect to traditional cooperative relaying strategies at no loss of diversity gain. In this paper, a novel cooperation protocol is developed based on complex-field wireless network coding. Sources transmit efficiently information symbols linearly combined with symbols from other sources. Different from existing wireless network coding protocols, transmissions are not restricted to binary symbols, and do not have to be received simultaneously. In a network with N sources, the developed protocol can achieve throughput up to approximately 1/N symbols per source per channel use, as well as diversity of order N. To deal with decoding errors at sources, selective- and adaptive-forwarding protocols are also developed at no loss of diversity gain. Analytical results corroborated by simulated tests show considerable performance gains with respect to distributed space-time coding, and bit-level network coding protocols.

This paper develops a cooperative scheme among cognitive radios (CRs) to increase the spectrum sensing performance. CRs adaptively transmit local binary decisions to a fusion center (FC), which in turn uses a simple maximum-likelihood detector to decide the presence of absence of the primary user (PU). The diversity order of the probability of false alarm and miss-detection is studied under both Neyman-Pearson and minimum-error-probability criteria. In particular, it is shown that under the Neyman-Pearson criterion, the probability of miss- detection can achieve diversity order up to the number of CRs for a bounded probability of false alarm. Under the minimum-error-probability criterion, both the probability of false alarm and miss-detection can achieve diversity order up to the number of CRs. Compared to existing cooperative sensing approaches, this novel scheme is robust to fading effects in both PU-to-CR and CR-to-FC links. Simulated tests verify the analytical claims, showing considerable performance gains compared to non-cooperative and non-adaptive hard-decision schemes.

This paper deals with clustering of spatially distributed data using wireless sensor networks. A distributed low-complexity clustering algorithm is developed that requires one-hop communications among neighboring nodes only, without local data exchanges. The algorithm alternates iterations over the variables of a consensus-based version of the global clustering problem. Using stability theory for time-varying and time-invariant systems, the distributed clustering algorithm is shown to be bounded-input bounded-output stable with an output arbitrarily close to a fixed point of the algorithm. For distributed hard K-means clustering, convergence to a local minimum of the centralized problem is guaranteed. Numerical examples confirm the merits of the algorithm and its stability analysis.

This paper develops algorithms to train linear support vector machines (SVMs) when training data are distributed across different nodes and their communication to a centralized node is prohibited due to, for example, communication overhead or privacy reasons. To accomplish this goal, the centralized linear SVM problem is cast as the solution of coupled decentralized convex optimization subproblems with consensus constraints on the parameters defining the classifier. Using the method of multipliers, distributed training algorithms are derived that do not exchange elements from the training set among nodes. The communications overhead of the novel approach is fixed and fully determined by the topology of the network instead of being determined by the size of the training sets as it is the case for existing incremental approaches. An online algorithm where data arrive sequentially to the nodes is also developed. Simulated tests illustrate the performance of the algorithms.

This paper deals with distributed demodulation of space-time transmissions of a common message from a multi-antenna access point (AP) to a wireless sensor network. Based on local message exchanges with single-hop neighboring sensors, two algorithms are developed for distributed demodulation. In the first algorithm, sensors consent on the estimated symbols. By relaxing the finite-alphabet constraints on the symbols, the demodulation task is formulated as a distributed convex optimization problem that is solved iteratively using the method of multipliers. Distributed versions of the centralized zero-forcing (ZF) and minimum mean-square error (MMSE) demodulators follow as special cases. In the second algorithm, sensors iteratively reach consensus on the average (cross-) covariances of locally available per-sensor data vectors with the corresponding AP-to-sensor channel matrices, which constitute sufficient statistics for maximum likelihood demodulation. Distributed versions of the sphere decoding algorithm and the ZF/MMSE demodulators are also developed. These algorithms offer distinct merits in terms of error performance and resilience to non-ideal inter-sensor links. In both cases, the per-iteration error performance is analyzed, and the approximate number of iterations needed to attain a prescribed error rate are quantified. Simulated tests verify the analytical claims. Interestingly, only a few consensus iterations (roughly as many as the number of sensors), suffice for the distributed demodulators to approach the performance of their centralized counterparts.

A multisource cooperative protocol is developed capable of achieving diversity order up to the number of cooperating users at a high throughput. In this design each source jointly encodes its own new information symbol with the information symbols received from other sources at past instants. Joint encoding is done using linear complex-field coefficients. Throughput analysis shows gains with respect to existing multi-source protocols and approaches the throughput of non-cooperative schemes. Diversity analysis shows that full spatial diversity is achievable. Simulations confirm the analytically established assessments.

Consider a set of sensors that wish to consent on the message broadcasted by a multi-antenna transmitter in the presence of white-noise jamming. The jammer's interference introduces correlation across receivers and destroys the decomposable form of the maximum-likelihood decoder, thus preventing direct application of known distributed detection algorithms. This paper develops distributed detectors that circumvent this problem. Treating the jammer signal as deterministic, we develop two distributed estimation-decoding algorithms. The first algorithm relies on the generalized likelihood ratio test, whereas the second algorithm relies on semi-definite relaxation techniques and is suitable for large alphabet sizes. Both algorithms feature: (i) distributed implementation requiring only single-hop communications; (ii) no constraints on the network topology so long as it is connected; and (iii) performance close to the optimum centralized detector in the presence of severe jamming.

The present paper develops a decentralized expectation-maximization (EM) algorithm to estimate the parameters of a mixture density model for use in distributed learning tasks performed with data collected at spatially deployed wireless sensors. The E-step in the novel iterative scheme relies on local information available to individual sensors, while during the M-step sensors exchange information only with their one- hop neighbors to reach consensus and eventually percolate the global information needed to estimate the wanted parameters across the wireless sensor network (WSN). Analysis and simulations demonstrate that the resultant consensus-based distributed EM (CB-DEM) algorithm matches well the resource- limited characteristics of WSNs and compares favorably with existing alternatives because it has wider applicability and remains resilient to inter-sensor communication noise.

When a terminal is recruited to cooperate with other neighboring terminals, its channel state and carrier frequency offset (CFO) may be unknown to the destination. Under these circumstances, this paper considers the use of distributed double-differential (DD) modulation, which simplifies receiver implementation because it by-passes channel and CFO estimation. Two double-differential codecs are proposed transmitting: i) across orthogonal channels using time-division multiplexing, achieving rate and error performance similar to that of co-located multi-antenna DD systems; or ii) simultaneously, benefiting from the distinct CFOs across terminals and bypassing the need of ordering protocols. Both (i)-(ii) approaches are considered in adaptive- and selective-relaying cooperation protocols demonstrating that maximum spatial diversity is achievable. Simulations corroborate the theoretical error performance claims.

Cooperative communication systems using various relay strategies can achieve spatial diversity gains, enhance coverage, and potentially increase capacity. For the practically attractive decode-and-forward (DF) relay strategy, we derive a high-performance low-complexity coherent demodulator at the destination in the form of a weighted combiner. The weights are selected adaptively to account for the quality of both source-relay-destination and source-destination links. Analysis proves that the novel coherent demodulator can achieve the maximum possible diversity, regardless of the underlying constellation. Its error performance tightly bounds that of maximum-likelihood (ML) demodulation, which provably quantifies the diversity gain of ML detection with DF relaying. Simulations corroborate the analysis and compare the performance of the novel decoder with existing diversity-achieving strategies including analog amplify-and-forward and selective-relaying.

We consider broadcasting to multiple destinations with uneven quality receivers. Based on their quality of reception, we group destinations in tiers and transmit using hierarchical modulations. These modulations are known to offer a practical means of achieving variable error protection of the broadcasted information to receivers of variable quality. After the initial broadcasting step, tiers successively re-broadcast part of the information they received from tiers of higher-quality to tiers with lower reception capabilities. This multi-tier cooperative broadcasting strategy can accommodate variable rate and error performance for different tiers but requires complex demodulation steps. To cope with this complexity in demodulation, we derive simplified per-tier detection schemes with performance close to maximum-likelihood and ability to collect the diversity provided as symbols propagate through diversified channels across successive broadcastings. Error performance is analyzed and compared to (non)-cooperative broadcasting strategies. Simulations corroborate our theoretical findings.

Combining multi-source cooperation and link- adaptive regenerative techniques, we develop a novel protocol capable of achieving diversity up to the number of cooperating users and larger coding gains without incurring the overhead of cyclic redundancy check (CRC) codes. The resulting protocol can be further optimized to take advantage of the information provided by CRC when available. Simulations confirm our theoretical assessments.

Differential encoding is known to simplify receiver implementation because it by-passes channel estimation. Relying on linear constellation precoders designed in closed-from for coherent multi-antenna systems, we derive a non-constant modulus space-time differential scheme that enables diversity, does not sacrifice rate, and more interestingly, it allows for constellation designs with many degrees of freedom. Performance merits of this scheme are analyzed and compared with existing differential designs. Simulations corroborate our theoretical findings.

Differential encoding is known to simplify receiver complexity because it by-passes channel estimation. However, over rapidly fading wireless channels, extra transceiver modules are necessary to enable differential transmission. Relying on a basis expansion model for time and frequency selective (doubly-selective) channels, we derive such a generalized block differential (BD) codec that achieves the maximum Doppler and multi-path diversity gains, while affording low-complexity maximum likelihood (ML) decoding. We further show that existing BD systems over frequency-selective or time-selective channels follow as special cases of our novel system. Simulations corroborate our theoretical analysis.

Differential encoding is known to simplify receiver implementation because it by-passes channel estimation. However, over rapidly fading wireless channels, extra transceiver modules are necessary to enable differential transmission. Relying on a basis expansion model for time and frequency selective (doubly selective) channels, we derive such a generalized block-differential (BD) codec and prove that it achieves maximum Doppler and multipath diversity gains, while affording low-complexity maximum-likelihood decoding. We further show that existing BD systems over frequency-selective or time-selective channels follow as special cases of our novel system. Simulations using the widely accepted Jakes' model corroborate our theoretical analysis.