The Complete Matlab Course for Wireless Comm. Engineering

This summary addresses key aspects of estimating Bit-Error-Rate (BER) performance in Single-Input-Single-Output Orthogonal Frequency Division Multiplexing (SISO-OFDM) systems under different channel conditions, mapping schemes, and transform techniques. Additionally, it covers Peak-to-Average Power Ratio (PAPR) estimation, Carrier Frequency Offset (CFO), Rayleigh fading channel modeling, and BER performance in Non-Orthogonal Multiple Access (NOMA) systems.

Estimating BER Performance Over SISO-OFDM (FFT) in AWGN Channel

For a SISO-OFDM system using Fast Fourier Transform (FFT), BER performance is evaluated over an Additive White Gaussian Noise (AWGN) channel. Different modulation mapping schemes such as Binary Phase Shift Keying (BPSK), Quadrature Amplitude Modulation (QAM), and Quadrature Phase Shift Keying (QPSK) are used to examine the system’s resilience to noise. The BER can be determined by transmitting symbols through the OFDM system, applying inverse FFT to modulate signals, and computing the ratio of incorrectly decoded bits.

Rayleigh Fading Channel and Jakes Fading Model

A Rayleigh fading channel can be modeled based on the Jakes fading model, which simulates multipath propagation, a key characteristic in wireless channels. This model assumes that the signal arrives at the receiver through multiple paths, each with a different phase and amplitude. The Jakes model generates fading coefficients that characterize the fluctuating signal amplitude and phase over time.

BER Estimation for SISO-OFDM (FFT) Over Rayleigh Fading Channel

In the absence of equalization, BER estimation over a Rayleigh fading channel involves transmitting the OFDM signal through the fading channel and analyzing the system’s degradation due to multipath propagation. The lack of equalization leads to significant performance loss. However, with equalization techniques like Zero Forcing (ZF) or Minimum Mean Square Error (MMSE), the channel impairments can be mitigated, improving BER performance by compensating for channel-induced distortion.

Carrier Frequency Offset (CFO) Problem

CFO arises from a mismatch between the transmitter and receiver oscillator frequencies, leading to inter-carrier interference (ICI) in OFDM systems. The performance impact of CFO is studied by estimating the Mean Square Error (MSE) of CFO estimation in an OFDM system using the Cyclic Prefix (CP) symmetry property. Both AWGN and Rayleigh fading channels are considered for this analysis.

BER Performance in SISO-OFDM Systems Based on DST and DCT

In addition to FFT-based OFDM, BER performance can be evaluated for systems employing Discrete Sine Transform (DST) and Discrete Cosine Transform (DCT) over AWGN and Rayleigh fading channels. Like the FFT-based system, various mapping schemes (e.g., BPSK, QPSK, QAM) are used. The inclusion of different equalizers (e.g., ZF, MMSE) further allows for performance comparison in Rayleigh fading channels.

PAPR Estimation for OFDM Systems

PAPR estimation is crucial in OFDM systems due to the high peak-to-average power inherent in multicarrier transmission. For OFDM systems based on FFT, DST, and DCT, PAPR is calculated by measuring the peak power of the transmitted signal relative to its average power. A comparative analysis of PAPR in systems using FFT, DST, and DCT reveals the potential advantages of alternative transforms in reducing PAPR, which is critical in improving the efficiency of power amplifiers.

BER Estimation in MIMO-OFDM Systems (Nt×Nr Configuration)

The study extends to multiple-input, multiple-output (MIMO) OFDM systems, where Nt represents the number of transmitting antennas, and Nr represents the number of receiving antennas. A general code for estimating BER in MIMO-OFDM systems based on FFT, DST, and DCT over a Rayleigh fading channel is provided. This allows for exploration of how spatial diversity in MIMO systems impacts BER performance compared to SISO systems.

NOMA in 5G and Beyond

Power Domain Multiplexing (PDM) and Successive Interference Cancellation (SIC) are explored as components of Non-Orthogonal Multiple Access (NOMA) systems in 5G. NOMA allows multiple users to share the same frequency band, enhancing spectral efficiency. The difference between interleaved and localized subcarrier mapping is also highlighted, as it impacts BER performance in NOMA systems.

BER Performance in Pre-coded Downlink NOMA Systems

The BER performance in FFT, DST, and DCT pre-coded downlink NOMA systems is examined using localized and interleaved subcarrier mapping schemes. This study explores how different transforms affect the efficiency of NOMA systems in handling multiple users under Rayleigh fading conditions.

PAPR in Pre-coded NOMA Systems

PAPR is also a concern in NOMA systems, where the selection of mapping schemes can influence the system’s power efficiency. PAPR estimation for FFT, DST, and DCT pre-coded NOMA systems with localized and interleaved subcarrier mapping is examined, allowing for a comparison of how different transforms affect power efficiency.

Conclusion

This summary covers the fundamental techniques for estimating BER and PAPR performance in OFDM systems using FFT, DST, and DCT over AWGN and Rayleigh fading channels. It emphasizes the importance of equalization, transform selection, and channel modeling, especially in modern MIMO and NOMA systems used in 5G communication. A comparison between various OFDM systems illustrates the trade-offs in performance and efficiency, essential for optimizing communication systems for future wireless standards.