Strong signals leaking from the transmitter increase the phase noise effect (caused by the local oscillator (LO) signal) and saturate the receiver, affecting the receiver performance. The transmitter signal leakage at the receiver must be eliminated or reduced as much as possible before reaching the RF stage of the receiver. Otherwise, the front-end circuit (low-noise amplifier and mixer section) must have a high dynamic range to receive the information signal against the strong transmitter leakage signal. In this paper, to eliminate the transmitter self-jamming signal on the receiver, the transmitter signal is sampled. Then, by compensating the amplitude and phase of the eliminating or pseudo-jammer signal, the amplitude and phase of this signal converge towards the amplitude and phase of the strong leakage signal, and the maximum elimination of the transmitter's strong leakage signal as self-jamming (jammer) occurs on the receiver. According to Figures (19 and 20), the gradient of the amplitude and phase coefficients in terms of the number of samples taken from the self-jamming signal using the steepest descent algorithm converged with less sampling, less time, and a higher slope of the curve, while in the reference method, the convergence of the amplitude and phase coefficients is not expressed and displayed. The convergence time of the steepest descent algorithm for the fastest downward slope is 68 µs. Also, the amount of elimination of the self-jamming signal in terms of phase is performed unstable and in more time, and an average of 44 dB of elimination is achieved. While in the innovative and new adaptive method based on the steepest descent algorithm algorithm, 51 dB of self-jamming signal from the transmitter on the receiver was eliminated, which is about 7 dB of elimination improvement compared to the reference method.