| Most existing works on distributed detection have assumed that a bank of independent dedicated channels or a multi-access channel is used for transmitting local decisions to the fusion center. While optimal local decision rules and fusion rules can be developed to optimize the detection performance for a given bandwidth constraint of the access channel, such a transmission scheme could result in significant energy expenditure when sensors are far from the fusion center. The natural solution to energy-efficient distributed detection is to use multi-hop transmission. We investigate two such options in this paper, and compare their detection performance (in terms of error exponent of average error probability), as well as energy expenditure with the parallel transmission scheme. We assume that sensors are uniformly distributed on a plane, and sensor observations are conditionally i.i.d. given the hypothesis. In the first scheme, each sensor quantizes its observation to k bits such that the Chernoff Information is maximized, and the quantized observations are transmitted to the fusion center through the Shortest Path Tree (SPT) without further processing at relaying nodes. This scheme achieves the same detection performance as parallel transmission, and offers some energy savings through multihop relaying. To further conserve the energy, in the second scheme, we force that each node, irrespective of a leaf node or an intermediate node on the transmission tree, transmit only $k$ bits to its next-hop neighbor. The optimal transmission structure in this case is given by the Minimum Spanning Tree (MST). A monotone likelihood-ratio quantizer (LRQ) is used to quantize sensor observations, and an intermediate node calculates the average LLR of its own observation and its descendents' observations, quantizes it again to k bits, and transmits it to its parent. We derive analytically the achievable error exponent for the second scheme, and show that for relatively large k, it achieves similar performance as parallel transmission schemes, but the energy consumption is significantly reduced. The result is verified with simulations of several detection problems of interest. |