# A Study on the Amplitude Comparison Monopulse Algorithm
## 1 Introduction  
Monopulse radar operates by comparing signal returns of four squinted beams steered around the expected target direction [1]. It is classified as amplitude comparison monopulse and phase comparison monopulse, and amplitude comparison monopulse is the most commonly used method, which detects azimuth and elevation deviation errors from the center of the track axis by comparing the amplitudes of the signal returns. Many methods have been proposed to improve the performance of monopulse algorithms in the literature [2; 3; 4; 5; 6; 7; 8; 9]. [PERSON] and [PERSON] [2] dealt with the problem of detecting and estimating the unknown angular position of the target observed simultaneously by controlling the number of antennas in the amplitude comparison monopulse radar, where the method is derived using a generalized likelihood ratio test. [PERSON] et al. [3] carried out a performance analysis according to antenna spacing using the phase comparison monopulse algorithm and proposed an efficient nonlinear antenna array based on the analysis results. [PERSON] et al. [4] showed the effect of the functional variables of the monopulse radar on angular tracking performance. [PERSON] and [PERSON] [5] showed the performance of amplitude comparison monopulse through simulation-based MSE (mean-square error) comparison with analytic MSE obtained by linearly approximating the nonlinear estimation equations. [PERSON] [6] carried out a performance analysis on the monopulse receivers in the secondary surveillance radar where the internal sources of error are considered. This paper discussed the general performance of the receiver of the monopulse radar where Gaussian noise is applied in the environment. [PERSON] and [PERSON] [7] analyzed the performance of an angle measurement of the monopulse radar with reception non-consistency. This paper showed that the performance of the angle measurement depends not only on the algorithm but also on the reception consistency. [PERSON] [8] discussed the estimation problem of the angle of arrival in thermal noise-applied amplitude comparison monopulse radar in terms of thecoherency of pulse returns. In [9], a novel methodology that overcomes the limitation of difference beam aided detection was proposed. While many monopulse algorithms are proposed so far to improve the estimation performance, most of them do not have clear relationships with the conventional algorithm, and only few conduct the performance analysis under the presence of measurement noise. Therefore, it is difficult to evaluate their performance improvement over the conventional algorithm under the measurement noise presence. Although some papers deal with formal noise analysis on the conventional algorithm, it is extremely complex, and no useful information comes from it. Motivated by these observations, this paper presents least-squares-based monopulse algorithms and a novel covariance prediction equation. The proposed algorithms have an iterative process that incrementally improves the accuracy of the conventional algorithm. It is shown that the conventional monopulse algorithm is a special case of the proposed algorithms with the first iterative step. The proposed covariance equation is simple but predicts very accurately the covariance of the estimated target location under the presence of measurement noise. This equation is independent of the measurement signal, and thus can be used to predict the performance of the monopulse algorithms before the algorithms are actually performed. This equation is also applicable to conventional monopulse algorithms, and quantitatively states estimation accuracy in terms of the major parameters of amplitude comparison monopulse radar. It is also important in in electronic warfare systems to predict the performance of amplitude comparison monopulse in terms of major parameters since intercepted signals from different types of radars are very often noisy and change depending on the mission being carried out and the task being performed [10; 11]. This paper is organized as follows.