A fundamental problem in wireless networks is determining the broadcast capacity, i.e., the maximum data transfer rate from a given node to every other node in a relay network. This paper studies the scaling of the broadcast capacity for a network with a single source and N destinations, of which f(N) are randomly selected to also act as relays. In high-density networks (i.e., the node density goes to infinity; the network area is fixed), it is shown that the broadcast capacity is upper bounded by Θ(log f(N)). Schemes are provided that achieve i) Θ(log f(N)) throughput if the channel fading is spatially continuous; ii) Θ(log log f(N)) throughput if the channel fading is spatially i.i.d.. For extended networks (i.e., the node density is fixed; the network area goes to infinity), the broadcast capacity is upper bounded by Θ(1) under channel models with fading and path-loss exponent α > 2. A multistage cooperative broadcasting scheme, which achieves Θ(1) broadcast rate for the high-density extended networks with pathloss channel model is proposed. These results quantifies the gains obtained due to cooperation compared to multihop noncooperative broadcasting, which has a maximum rate that scales as Θ(1) for high-density and Θ(1/(log f(N))α/2) for extended networks.

Cognitive radios aim to coexist in the unused spectrum bands which are licensed to primary users without harming the primary transmission/reception. For a cognitive radio, it is important to detect the band in which the primary is operating as fast as possible and with high reliability in order to adapt its transmission. In this work, we proposeP-partitioningmethodin combination with energy detectors for the search of the band that the primary user is operating. In the P-partitioning method, the spectrum bands are categorized into P groups and the group that the primary band belongs to is detected in a recursive fashion. The energy detector operates on each group and the test statistics is the total energy received in the bands belonging to the group. The proposed search technique has detection timePlogP(N), whereNis the number of bands in the spectrum. WhenP=N, the proposed scheme is equivalent to linear search with detection time N. We study the performance of the proposed scheme for a single non-cooperative radio and also for multiple cooperating radios. For a single cognitive radio, we provide an upper bound on the probability of correct detection which presents two different regimes of operation. In the low SNR regime, although it is counter-intuitive the partitioning improves the probability of detection. This is due an averaging effect when the signal energy in different bands are accumulated to obtain the energy contribution from a group. In the high SNR regime, performance degrades with partitioning. In addition, we observe that user cooperation improves the performance in the high SNR regimes.

Recently, we proposed a decentralized cooperative communication scheme [1]. In this paper we show that randomized decentralized schemes perform well even when the cooperating nodes are asynchronous. In particular we study the attainable diversity for frequency selective channels, and the coding gain in comparison to a centralized scheme.

In this work, we study a communication scheme in which nodes transmit sufficient statistics of their observations over non-orthogonal medium access channels for distributed estimation. This scheme unifies and generalizes several multiple access schemes such as uncoded transmissions of Gaussian observations and type-based multiple access. For the exponential family of distributions, we show that the sufficient-statistic based multiple access (SSBMA) achieves the Cramer-Rao bound on the estimation error asymptotically. Further, we argue that such an optimality result only applies to the exponential family of distributions. In addition, we present a simplified and unified analysis of asymptotic distribution of estimation error for a very general class of communication schemes and estimators. The proposed analysis method reduces the computation of asymptotic estimation error to mere calculation of derivatives. With the proposed technique, we analyze the performance of various communication schemes with optimal and suboptimal estimators and with i.i.d. (independent and identically distributed) data.

A fundamental problem in large scale wireless networks is the energy efficient broadcast of source messages to the whole network. The energy consumption increases as the network size grows, and the optimization of broadcast efficiency becomes more important. In this paper, we study the optimal power allocation problem for cooperative broadcast in dense large-scale networks. In the considered cooperation protocol, a single source initiates the transmission and the rest of the nodes retransmit the source message if they have decoded it reliably. Each node is allocated an-orthogonal channel and the nodes improve their receive signal-to-noise ratio (SNR), hence the energy efficiency, by maximal-ratio combining the receptions of the same packet from different transmitters. We assume that the decoding of the source message is correct as long as the receive SNR exceeds a predetermined threshold. Under the optimal cooperative broadcasting, the transmission order (i.e., the schedule) and the transmission powers of the source and the relays are designed so that every node receives the source message reliably and the total power consumption is minimized. In general, finding the best scheduling in cooperative broadcast is known to be an NP-complete problem. In this paper, we show that the optimal scheduling problem can be solved for dense networks, which we approximate as a continuum of nodes. Under the continuum model, we derive the optimal scheduling and the optimal power density. Furthermore, we propose low-complexity, distributed and power efficient broadcasting schemes and compare their power consumptions with those-of-a traditional noncooperative multihop transmission.

We study the problem of designing distributed space-time codes for cooperative communication. A major challenge in distributed cooperative transmissions is to find a way to coordinate the relay transmissions without requiring extra control information overhead. Most of the previous works on the subject assume each node emulates a predetermined antenna of a multiple-antenna system. However, this requires a centralized "antenna allocation" procedure. Here, we introduce randomized strategies that decentralize the transmission of a space time code from a set of distributed relays. The simple idea we propose is to let each node transmit a random linear combination of the codewords that would be transmitted by all the antennas in a centralized space time coding scheme. We provide different code designs that achieve the diversity order (min(N, L)) when number of nodes N is different than the number of virtual antennas L. In this paper, we focus on the case when N = L and we show that under certain designs the achieved diversity order is fractional

In this paper, we study the problem of designing distributed space-time codes for cooperative communication. We introduce randomized strategies that decentralize the transmission of a space time code from a set of distributed relays and analyze their performance. In our methods, as in other cooperative transmission strategies, the relay signals are encoded so as to provide diversity and coding gains. However, our methods enable the relays to act independently and to achieve such gains in a decentralized fashion. The simple idea we propose is to let each node transmit a random linear combination of the codewords that would be transmitted by all the antennas in a centralized space time coding scheme. Different decentralized strategies correspond to different choices for the statistics of the random coefficients. We provide sufficient conditions on the distributions of the random coefficients and on the number of nodes that guarantee to achieve the maximum diversity gain. We show that the proposed scheme achieves full diversity (N) if NL.

We study error propagation in wireless cooperative broadcast protocols. In our model, nodes in the network are randomly deployed in a fixed region. The message from a certain source node is relayed by multiple groups of cooperating relays that are located in predetermined consecutive swaths of the network area. We refer to these groups of relays as "levels". Our analysis is based on the derivation of recursive equations that express the error rate at each relay in a given level as a function of the error probabilities of the nodes in the previous levels. To provide analytical results we take the limit as the number of nodes goes to infinity while the relay power goes to zero, so that the relay power density per unit area is constant. In the limit, we show that the relay power density and area of the regions that correspond to the levels lead to fixed points in the error rate that prevent catastrophic error propagation, regardless of the distance the message is transmitted over.

We study the optimal power allocation problem for cooperative broadcast in dense large-scale networks. In our set-up, a single source initiates the transmission and the nodes that receive the message with sufficient signal-to-noise ratio (SNR) retransmit. The goal is to design the transmission order (schedule) and the transmission powers of the relays so that the message reaches to the entire network with the minimum possible power expenditure. In general, finding the best scheduling in cooperative broadcast is known to be NP-complete. In this paper, we show that the optimal scheduling is easily resolved for certain network topologies and channel models. Furthermore, we approximate dense large-scale networks with a continuum of nodes and provide optimal power density for the continuum network under pathloss attenuation

Cooperative broadcast aims to deliver a source message to a locally connected network by means of collaborating nodes. In traditional architectures, node cooperation has been at the network layer. Recently, physical layer cooperative schemes have been shown to offer several advantages over the network layer approaches. This form of cooperation employs distributed transmission resources at the physical layer as a single radio with spatial diversity. In decentralized cooperation schemes, collaborating nodes make transmission decisions based on the quality of the received signal, which is the only parameter available locally. In this case, critical parameters that influence the broadcast performance include the source/relay transmission powers and the decoding threshold (the minimum signal-to-noise ratio (SNR) required to decode a transmission). We study the effect of these parameters on the number of nodes reached by cooperative broadcast. In particular, we show that there exists a phase transition in the network behavior: if the decoding threshold is below a critical value, the message is delivered to the whole network. Otherwise, only a fraction of the nodes is reached, which is proportional to the source transmit power. Our approach is based on the idea of continuum approximation, which yields closed-form expressions that are accurate when the network density is high.

We consider a wireless network in which a single source transmits its message with the help of multiple cooperative relays. In our model, the source broadcasts the message and the relays retransmit it as soon as they are able to produce an inference of acceptable quality. If the network is dense, multiple nodes quasi-synchronously retransmit the source message, acting as groups of cooperative relays, thereby increasing the range of transmission. We analyze the behavior of such cooperative networks with respect to parameters such as the source and relay transmission powers by deriving a dynamic system model using a continuum asymptote as the number of relay nodes goes to infinity. The methodology developed can be used to analyze the performance of other cooperative protocols.

We consider a multi-hop wireless network in which a single source-destination pair communicates with the help of multiple cooperative relays. The relays deliver the source message by transmitting it in groups at every hop. The group transmissions increase the signal-to-noise ratio (SNR) of the received signal, and improve the range of communication. In this paper, we analyze the behavior of cooperative network with respect to the network parameters such as source/relay transmission powers and the decoding threshold (the minimum SNR required to decode a transmission). It is shown that if the decoding threshold is below a critical value, the message is delivered to the destination regardless of the distance between the source and the destination. Otherwise, the number of transmitting nodes diminishes at every hop, and the message does not reach to a destination far away. Our approach is based on the idea of continuum approximation, which is valid when the network density is high.

Cooperative transmission schemes in multi-hop networks have the advantage of energy efficiency and increased network coverage. Realizing these advantages, however, requires a compatible physical layer. We consider the detection of a signal transmitted by multiple cooperative nodes. Exploiting the structure of the network, we formulate the problem, and propose a generalized likelihood ratio detector. We compare the performance of the proposed detector with two others: estimator-correlator and a genie-aided detector (provides a performance benchmark). The genie-aided detector assumes the knowledge of certain network parameters which may be unknown during reception. Simulations show that the proposed detector performs reasonably close to the genie-aided one, while being considerably better than the estimator-correlator.

Hyperspectral image processing is a pixel-by-pixel approach to the detection and localization of features by spectral analysis techniques. Usually, partial knowledge about the feature, noise, and clutter spectra are provided, and the problem is to 'unmix' each pixel, or to estimate the relative concentrations of the reference spectra on a per pixel basis. A popular method of linear spectral unmixing for hyperspectral imagery is linear least squares. Linear least square approaches are appropriate when observational errors predominate and are inappropriate when significant modeling errors are present. The least square approach has some disadvantages, especially in cases with few, poorly known references or significant reference variation throughout an image. In this article, the restricted total least squares (RTLS) approach is presented and evaluated on experimental data. Although the proposed RTLS require more calculations than linear least squares, its relative error performance is much better.