OVERVIEW

Objectives – Methods – Accomplishments

Our motivation in studying the design of space-time modulation for sensor networks stems from the fact that transmit and receive diversity greatly improve achievable performance in the wireless channel. Thus, by cooperating, sensor nodes can transmit more information across the network or, alternatively improve performance dramatically. Space-time code design has typically been accomplished via the optimization of the Chernoff/union bound on the probability of error; however this metric is loose at low SNR. We have devised two methods for tighter bounding on the probability of error: expurgating the union bound (indecomposable union bound, IUB) to remove redundant events and a progressive union bound (PUB) coupled with a saddlepoint approximation. The IUB provides a simple way of deriving a tighter performance bound from the union bound directly, but does not always achieve large gains due to the fact that not all code sets can be easily expurgated. The PUB offers the tightest performance bound and furthermore, by varying parameters of the PUB, the PUB approach allows a tradeoff between accuracy and numerical complexity. These new bounds have been used to design space-time block codes for low SNRs which yield improved performance over the union bound based schemes. In a sensor network framework, for nodes to cooperate, they must exchange information. There has been some recent work that considers the relaying of information from a source node to a destination node via helper nodes. At the helpers, the message is simply amplified and transmitted to the destination. This scheme results in amplifying the noise in the original received message. We have two results in this area: the first is to show rigorously that this amplify-and-forward scheme proposed by Hua 2003, does in fact achieve a diversity level equal to the number of relaying nodes (this was conjectured via experiments) and the second is to devise a decode-and-forward scheme which offers improved performance (0.5 to 0.75dB gain) over the amplify-and-forward scheme. In the Hua scheme, only orthogonal-type space-time block codes could be employed, which is a significant restriction due the limited number of such code sets; however, in our coding scheme arbitrary good code sets can be employed and retain diversity.

FUTURE DIRECTIONS

In area (e), our current approach to the decode-and-forward scheme is to employ an encoding strategy at the helper nodes that is based on existing high-performance space-time block codes. However, such designs are not matched to the scenario of having noisy observations at the transmitting nodes. Thus, our goal is to exploit our previous work on bounding the performance of space-time decoders to achieve tight bounds for the scenario for noisy observations at the transmitter and thus develop space-time block encoding strategies that are completely specific to the sensor-network scenario. An element of space-time block code design that is not well-treated is that where the number of cooperating nodes (antenna elements) is time-varying due to node failures. Thus we shall also consider the scenario where the number of cooperating nodes is not known a priori. Finally, we wish to evaluate the fundamental achievable performance of such cooperative communication schemes so that we can benchmark our proposed schemes. We conjecture that a practical scheme for cooperative communications will be some combination of a simple relaying protocols with more sophisticated encoding and decoding.

PEOPLE

FACULTY

U. Mitra

GRADUATE STUDENT

M. Vajapeyam