Wireless communication systems are based on frequency synthesizers that generate carrier signals, which are used to transmit information. Frequency synthesizers use voltage controlled oscillators (VCO) to produce the required frequencies within a specified period of time. In the process of generating frequency, the VCO and other electronic components such as amplifiers produce some unwanted short-term frequency variations, which cause frequency instability within the frequency of interest known as phase noise (PN). PN has a negative impact on the performance of the overall wireless communication system. A literature study conducted on this research reveals that the existing PN cancellation techniques have some limitations and drawbacks that require further attention. A new PN correction technique based on the combination of least mean square (LMS) adaptive filtering and single-loop single-bit Sigma Delta (SD) modulator is proposed. The new design is also based on the Cascaded Resonator Feedback (CRFB) architecture. The noise transfer function (NTF) of the architecture was formulated in way that made it possible to stabilize the frequency fluctuations within the in-band (frequency of interest) by locating its poles and zeros within the unit circle. The new design was simulated and tested on a commercially available software tool called Agilent Advanced Design System (ADS). Simulation results show that the new technique achieves better results when compared with existing techniques as it achieves a 104 dB signal-to-noise (SNR), which is an improvement of 9 dB when compared with the existing technique accessed from the latest publications. The new design also achieves a clean signal with minimal spurious tones within the inband with a phase noise level of -141 dBc/Hz (lower phase noise level by 28 dBc/Hz) when compared with the existing techniques. / Thesis (MEng)--University of Pretoria, 2017. / Electrical, Electronic and Computer Engineering / MEng / Unrestricted