Multistatic search theory

The characterizing feature of multistatic sensor systems is the inclusion of geographically independent receivers that might receive echoes from any source. We develop a simple analytic theory to predict detection probability, and use it to study pattern optimization, cost/effectiveness, reliability and the relative attractiveness of multistatic versus monostatic systems. INTRODUCTION A typical monostatic radar or sonar sensor includes one transmitter or source (Tx) and one receiver (Rx). Tx emits pulses that travel to a target and are reflected from it. Rx detects the reflected pulses, and the time difference between transmission and reception determines the distance to the target. Tx and Rx are co-located, and may even use the same antenna. The range ρ of the sensor is the largest distance at which detection is possible. At its simplest, barring complications due to topography or directional background noise, one can visualize the effect of each sensor as a covered circle with radius ρ. Much of our intuition about search is built on this idea of individual covered areas. For example 1. A barrier can be constructed by using multiple sensors whose circles slightly overlap. 2. The area covered by a system of sensors is easily illustrated on a map. 3. If you move one sensor, there is no effect on the others. A multistatic system incorporates multiple sources and receivers that are not paired. Any Rx can receive reflected transmissions from any Tx, and they can be present in different numbers. Figure 1 illustrates the basic structure of a monostatic sensor and a multistatic system. Here are some arguments in favor of multistatic sonar systems: 1. Receivers are less expensive than sources (Amanipour & Olfat, 2011), so it makes sense to employ more receivers than sources. For example, the U.S. Navy’s SSQ-125 active sonobuoy costs about five times as much as the SSQ-53 passive sonobuoy, one of the sonobuoy types that can listen for its signals (Signal Online, 2012; USN, 2014). 2. A multistatic system can employ different platforms for sources and receivers. A ship might be Tx, while Rx is a sonobuoy. 3. Sources reveal their locations when they transmit, and targets can use that information to avoid detection. However, the independent receivers in a multistatic system do not reveal their positions.