Carrier Frequency Offset in Double Sideband Suppressed Carrier Modulation: Proposed Method

Abstract

This paper presents an analysis of Carrier Frequency Offset (CFO) in Double Sideband Suppressed Carrier (DSB SC) modulation systems. I investigated the impact of CFO on signal quality and propose a method for its detection and compensation. The study includes simulations of the modulation process, introduction of CFO, and subsequent compensation techniques. Results demonstrate the effectiveness of the proposed method in mitigating the effects of CFO in DSB SC systems.

1. Introduction

Double Sideband Suppressed Carrier (DSB SC) modulation is a technique widely used in communication systems due to its power efficiency. However, like many modulation schemes, it is susceptible to Carrier Frequency Offset (CFO), which can significantly degrade signal quality. This paper explores the effects of CFO on DSB SC systems and presents a method for its detection and compensation.

2. System Model

2.1 Transmitter

The transmitter model consists of the following components:

  1. Bit Generation: A sequence of 1024 random bits is generated.

  2. Pulse Shaping: Bits are mapped to symbols (+1 for bit 1, -1 for bit 0) and shaped using a raised cosine filter.

  3. Modulation: The shaped signal is multiplied with a carrier frequency of 20 GHz.

Key parameters:

  • Sampling frequency (Fs): 160 GHz

  • Symbol rate (Rs): 20 GHz

  • Samples per symbol (sps): 8

  • Carrier frequency (fc): 20 GHz

  • Signal-to-Noise Ratio (SNR): 7 dB

2.2 Channel

The channel introduces Additive White Gaussian Noise (AWGN) and a carrier frequency offset of 50 MHz.

2.3 Receiver

The receiver performs the following operations:

  1. Demodulation: The received signal is multiplied with a local oscillator.

  2. Filtering: A Butterworth filter is applied to remove high-frequency components.

  3. CFO Detection: Autocorrelation and periodogram analysis are used to detect CFO.

  4. Compensation: The detected CFO is used to adjust the local oscillator frequency.

  5. Envelope Detection: Hilbert transform is applied to extract the signal envelope.

3. Methodology

3.1 CFO Detection

The CFO detection algorithm follows these steps:

  1. Compute the autocorrelation of the received signal.

  2. Normalize the autocorrelation to zero mean.

  3. Square the normalized autocorrelation.

  4. Compute the periodogram of the squared autocorrelation.

  5. Identify peaks in the periodogram using a threshold-based approach.

  6. Extract the carrier frequency and CFO from the peak locations.

3.2 CFO Compensation

CFO compensation is achieved by adjusting the frequency of the local oscillator at the receiver based on the detected CFO.

4. Results and Analysis

4.1 Modulation and Demodulation

The time and frequency domain representations of the modulated signal are presented, showing the characteristic double sideband structure of DSB SC modulation.

4.2 CFO Detection

The autocorrelation and periodogram analysis results are shown, demonstrating the effectiveness of the proposed method in detecting the introduced CFO of 50 MHz.

4.3 CFO Compensation

Comparisons of the signal spectrum before and after CFO compensation are presented, illustrating the improvement in signal quality after compensation.

4.4 Bandwidth Analysis

An optional bandwidth analysis is included, showing how the system bandwidth can be estimated from the received signal spectrum.

5. Conclusion

This study demonstrates the significant impact of Carrier Frequency Offset on DSB SC modulation systems and presents an effective method for its detection and compensation. The proposed technique, based on autocorrelation and periodogram analysis, successfully identifies the CFO and enables its compensation, leading to improved signal quality.

6. Future Work

Future research directions may include:

  1. Analysis of the proposed method's performance under various SNR conditions.

  2. Investigation of alternative CFO detection and compensation techniques.

  3. Extension of the study to other modulation schemes.

References

  1. Proakis, J. G., & Salehi, M. (2008). Digital Communications. McGraw-Hill.

  2. Rappaport, T. S. (2002). Wireless Communications: Principles and Practice. Prentice Hall.

  3. MATLAB Documentation. (2023). Signal Processing Toolbox.

(Do refer Documentation for better understanding and Visualization)

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