On Cooperative Beamforming Based on Second-Order Statistics of Channel State Information

Cooperative beamforming in relay networks is considered, in which a source transmits to its destination with the help of a set of cooperating nodes. The source first transmits locally. The cooperating nodes that receive the source signal retransmit a weighted version of it in an amplify-and-forward (AF) fashion. Assuming knowledge of the second-order statistics of the channel state information, beamforming weights are determined so that the signal-to-noise ratio (SNR) at the destination is maximized subject to two different power constraints, i.e., a total (source and relay) power constraint, and individual relay power constraints. For the former constraint, the original problem is transformed into a problem of one variable, which can be solved via Newton's method. For the latter constraint, the original problem is transformed into a homogeneous quadratically constrained quadratic programming (QCQP) problem. In this case, it is shown that when the number of relays does not exceed three the global solution can always be constructed via semidefinite programming (SDP) relaxation and the matrix rank-one decomposition technique. For the cases in which the SDP relaxation does not generate a rank one solution, two methods are proposed to solve the problem: the first one is based on the coordinate descent method, and the second one transforms the QCQP problem into an infinity norm maximization problem in which a smooth finite norm approximation can lead to the solution using the augmented Lagrangian method.Comment: 30 pages, 9 figure

Measurement Matrix Design for Compressive Sensing Based MIMO Radar

In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to a fusion center, where an L1-optimization problem is formulated and solved for target information. CS-based MIMO radar exploits the target sparsity in the angle-Doppler-range space and thus achieves the high localization performance of traditional MIMO radar but with many fewer measurements. The measurement matrix is vital for CS recovery performance. This paper considers the design of measurement matrices that achieve an optimality criterion that depends on the coherence of the sensing matrix (CSM) and/or signal-to-interference ratio (SIR). The first approach minimizes a performance penalty that is a linear combination of CSM and the inverse SIR. The second one imposes a structure on the measurement matrix and determines the parameters involved so that the SIR is enhanced. Depending on the transmit waveforms, the second approach can significantly improve SIR, while maintaining CSM comparable to that of the Gaussian random measurement matrix (GRMM). Simulations indicate that the proposed measurement matrices can improve detection accuracy as compared to a GRMM

Compressive Sensing for MIMO Radar

Multiple-input multiple-output (MIMO) radar systems have been shown to achieve superior resolution as compared to traditional radar systems with the same number of transmit and receive antennas. This paper considers a distributed MIMO radar scenario, in which each transmit element is a node in a wireless network, and investigates the use of compressive sampling for direction-of-arrival (DOA) estimation. According to the theory of compressive sampling, a signal that is sparse in some domain can be recovered based on far fewer samples than required by the Nyquist sampling theorem. The DOA of targets form a sparse vector in the angle space, and therefore, compressive sampling can be applied for DOA estimation. The proposed approach achieves the superior resolution of MIMO radar with far fewer samples than other approaches. This is particularly useful in a distributed scenario, in which the results at each receive node need to be transmitted to a fusion center for further processing

Cooperative Beamforming for Wireless Ad Hoc Networks

Via collaborative beamforming, nodes in a wireless network are able to transmit a common message over long distances in an energy efficient fashion. However, the process of making available the same message to all collaborating nodes introduces delays. In this paper, a MAC-PHY cross-layer scheme is proposed that enables collaborative beamforming at significantly reduced collaboration overhead. It consists of two phases. In the first phase, nodes transmit locally in a random access time-slotted fashion. Simultaneous transmissions from multiple source nodes are viewed as linear mixtures of all transmitted packets. In the second phase, a set of collaborating nodes, acting as a distributed antenna system, beamform the received analog waveform to one or more faraway destinations. This step requires multiplication of the received analog waveform by a complex weight, which is independently computed by each cooperating node, and which allows packets bound to the same destination to add coherently at the destination node. Assuming that each node has access to location information, the proposed scheme can achieve high throughput, which in certain cases exceeds one. An analysis of the symbol error probability corresponding to the proposed scheme is provided.Comment: 5 pages, 4 figures. To appear in the Proceedings of the IEEE Global Communications Conference (GLOBECOM), Washington, DC, November 26 - 30, 200

Blind Estimation of Multiple Carrier Frequency Offsets

Multiple carrier-frequency offsets (CFO) arise in a distributed antenna system, where data are transmitted simultaneously from multiple antennas. In such systems the received signal contains multiple CFOs due to mismatch between the local oscillators of transmitters and receiver. This results in a time-varying rotation of the data constellation, which needs to be compensated for at the receiver before symbol recovery. This paper proposes a new approach for blind CFO estimation and symbol recovery. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual Multiple-Input Multiple-Output (MIMO) problem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently transform the multiple CFOs estimation problem into many independent single CFO estimation problems. Furthermore, an initial estimate of the CFO is obtained from the phase of the MIMO system response. The Cramer-Rao Lower bound is also derived, and the large sample performance of the proposed estimator is compared to the bound.Comment: To appear in the Proceedings of the 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Athens, Greece, September 3-7, 200

Modified Partition Functions, Consistent Anomalies and Consistent Schwinger Terms

A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this modified partition function naturally.Comment: 25 page