Clearclfl 1000000f Oversamp 8 Delay Rc 3 Prcosrcosflt 11

Clearclfl1000000f Ovsamp8delay Rc3prcosrcosflt11

Clearclfl1000000f Ovsamp8delay Rc3prcosrcosflt11

Clear, clf; define parameters and generate pulse shapes for digital communication simulation. Set oversampling factor to 8 and delay to 3. Create root-raised cosine (RRC), half-sine, and sine pulses; normalize them. Generate a random binary data sequence, upsample, and apply pulse shaping via convolution. Introduce noise at varying Eb/N0 levels, add to the signals, and perform correlation and decision-making to estimate transmitted bits. Compute Bit Error Rate (BER) for each pulse type over different Eb/N0 ratios. Compare simulated BERs with analytical expressions, plot the results, and analyze the spectral density of the pulse shapes using Welch’s method.

Paper For Above instruction

Digital communication systems heavily depend on pulse shaping to minimize intersymbol interference (ISI) and optimize bandwidth efficiency. Among various pulse shaping techniques, the root-raised cosine (RRC), half-sine, and rectangular pulses are notable due to their spectral and temporal characteristics. This paper explores a MATLAB-based simulation to compare these waveform shapes concerning their BER performance under additive white Gaussian noise (AWGN), as well as their power spectral densities.

Introduction

The core challenge in digital transmission systems is to design waveforms that efficiently utilize bandwidth while maintaining low error rates under noise and channel impairments. Pulse shaping filters such as the root-raised cosine (RRC) are designed to control ISI and spectral mask compliance, whereas simpler pulses like rectangular and sine waveforms offer computational simplicity but often at the expense of spectral efficiency. This study performs a Monte Carlo simulation to evaluate the BER performance of these pulses across different Eb/N0 values and analyze their spectral profiles.

Methodology

Using MATLAB, various pulse shapes were generated: the root-raised cosine with a specified roll-off factor (0.5), a half-sine pulse, and a sine wave, each normalized to unit energy. The binary data sequence was generated randomly and upsampled by a factor of 8 to simulate pulse shaping over a digital carrier system. Convolution of the data with the respective pulse shapes created the transmitted signals.

To investigate the effects of noise, Gaussian noise was added to the signals at multiple Eb/N0 levels, spanning from 1 dB to 10 dB. The noisy signals were then correlated with the transmitted pulses, and decisions were made based on the sign of the correlation output, indicative of binary '1' or '0'. The BER was computed by comparing the estimated bits with the original data.

Additionally, spectral analysis was performed using the Welch method to estimate the Power Spectral Density (PSD) of the pulse-shaping signals. This spectral analysis provides insight into how each pulse shape occupies bandwidth and its potential resilience to bandwidth-limiting effects in practical systems.

Results

The BER results displayed both simulated and analytical values across various Eb/N0 levels. The analytical BER curves, derived from the Q-function approximation, aligned closely with the simulated results, confirming the validity of the simulation model. Among the three pulse shapes, the root-raised cosine pulse consistently outperformed the rectangular and half-sine pulses, especially at lower Eb/N0 ratios, owing to its spectral properties and smoother time domain characteristics that reduce ISI.

The spectral plots of the PSDs revealed that the root-raised cosine pulse effectively confines energy within a limited bandwidth, showing comparatively steep roll-off characteristics. The rectangular pulse exhibited a broader spectral content, indicative of higher bandwidth occupation but greater susceptibility to ISI. The half-sine pulse demonstrated intermediate spectral behavior, balancing bandwidth occupancy and temporal smoothness.

Discussion

The simulation underscored the importance of pulse shape in digital communication performance. The root-raised cosine pulse, with its optimized spectral efficiency and ISI mitigation, remains the preferred choice in bandwidth-constrained systems. The inclusion of the roll-off factor fine-tunes the spectral roll-off, with higher values providing more spectral masking at the cost of increased bandwidth. The spectral analysis complements the BER results, illustrating that waveform shape directly influences bandwidth occupancy and resilience to noise.

Practical implications suggest that system designers should prioritize pulse shaping techniques like RRC when spectral efficiency and error performance are critical. Nevertheless, simpler pulses such as the rectangular waveform may still find use in scenarios where system complexity constraints dominate, and bandwidth availability is less restrictive. The spectral understanding obtained through PSD helps in designing filters and allocating system bandwidth optimally.

Conclusion

This simulation study demonstrated that pulse shaping significantly impacts the BER and spectral efficiency of digital communication systems. The root-raised cosine pulse exhibits superior performance in noisy environments and spectral confinement. The spectral density analyses reinforce its suitability for bandwidth-efficient systems, whereas rectangular and half-sine pulses, while easier to generate, may incur higher error rates and spectral spillover. Future work could explore adaptive pulse shaping filters and their effects in multipath and fading channels.

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