# Precision of 3-Configurations with Respective Sub-Configurations of 2-Ring Concentric Planar Array in Direction Finding

### Abstract

*Direction finding is a key area of sensor array processing which is encountered in a broad range **of important engineering applications. These applications include wireless communication, rada and sonar,* *among others. This work compares estimation accuracy of 3-configurations (based on the inner* *radius variation and constant outer radius) of a uniform 2-ring concentric planar array in direction* *finding via the Cramer-Rao bound derivation and analysis. The 3-configurations’ estimation accuracy is articulated to their respective sub-configurations based on the sensors distribution in each ring. The* *sub-configurations use equal overall number of sensors (multiple of 4) but with **60% *- *40% **distribution, **50% *- *50%* *distribution and **40% *- *60% **distribution on the inner-outer rings respectively. It is found that the* *estimation accuracy increases as the inner radius approaches the outer radius and thus configuration three** (where the inner radius equals three-quarters of the outer radius) **has the best precision in direction finding compared to configuration two **(where the inner radius equals half of the outer radius) and configuration one (where the inner radius equals one-quarter of the outer radius)**. Furthermore, based on the sub-configurations (where there is varying sensor distribution along the two rings),** sub-**configuration three **(where 40% of the sensors are distributed along the inner radius and 60% of the sensors are distributed along the outer radius) **is found to have the best estimation accuracy compared to the other two sub-configurations (**50% *- *50% and 60% *- *40% distributions, respectively**). It is observed that the closer the inner radius approaches the outer radius and/or the lower the inner-outer radius’ sensor ratio, the better the estimation accuracy. It is thus recommended that all sensors should be distributed along the outer radius for better estimation accuracy. These findings would help* *direction finders such as engineers to economically utilize a given number of sensors.*