The Synthetic Impulse and Aperture Radar (SIAR) is an advanced radar system which utilizes different orthogonal carrier frequencies. As a four-dimensional (4-D) radar, SIAR offers numerous advantages such as protection against anti-radiation missiles (ARM), detection of stealth targets, low probability of interception (LPI), and tracking of multiple targets. However, one of the key challenges facing these radars is the coupling between range and angle measurements, where errors in range measurements can impact angle measurements and vice versa. To tackle this issue, radar designers commonly develop transmitting waveforms based on carrier frequency coding to minimize the coupling. Various methods, including random frequency coding, sequential frequency coding, and positive and negative sequential frequency coding, have been proposed to reduce the coupling between range and angle measurements for two-dimensional (2-D) linear arrays. This article focuses on extending these ideas to circular arrays (3D radar) and introduces a method known as positive and negative random carrier frequency coding. We take advantage of random code and the concept of positive-negative frequency coding. Additionally, mathematical equations and simulations demonstrate that the coupling between azimuth angle and elevation angle is independent of the frequency coding type and remains consistent across all conditions. Through our research, we demonstrate that the proposed method effectively reduces coupling by approximately 40% more than other frequency coding methods. In the proposed method, we combine output of two consecutive periods by an approach similar to what happens in pulse integration in radar, so we don't require complex computations or new hardware. This method has another advantage such as pulse-to-pulse frequency agility, enhancing protection against ARM through virtual displacement of transmitters. Circular arrangements ensure simultaneous coverage of the entire space.