Received Signal
Time Domain:
y(t)=[h(t)]∗s(t)+w(t)
Where:
· h(t) = Channel Impulse Response (due to Multi-path Rayleigh Fading)
s(t): Transmitted signal
· ∗: Convolution operator
· w(t): Additive noise
Frequency Domain:
Y(ω) = H(ω)⋅S(ω)+W(ω)
Where:
· Y(ω): Received signal spectrum
· H(ω),S(ω),W(ω): Fourier Transforms of the respective time-domain signals
Digital Communication with Channel Equalization and Demodulation: Overcoming Rayleigh Fading and AWGN
Digital communication system with channel equalization and demodulation involves transmitting a modulated signal through a channel affected by Rayleigh fading and AWGN. Equalization mitigates signal distortion, and demodulation extracts the original message signal, ensuring reliable data recovery.
Understanding the digital communication process involves several key stages. Each stage is crucial for ensuring that the message signal is transmitted effectively and accurately. Below is a detailed overview of each stage in the process:
- Message Signal: This is the original data or information that needs to be transmitted from the sender to the receiver. It can be in the form of text, audio, video, or any other type of data. The message signal is the input to the communication system, representing the content that the sender wants to convey.
Fig: Original Message Signal
Fig: Carrier Signal - Modulation: To prepare the message signal for transmission over a communication channel, it must be modulated onto a carrier signal. Modulation involves varying the carrier signal's properties (such as amplitude, frequency, or phase) in accordance with the message signal. This process helps in effectively transmitting the signal over long distances and through various mediums. Common modulation techniques include Amplitude Modulation (AM), Frequency Modulation (FM), and Phase Modulation (PM).
- Channel (with Rayleigh Fading and AWGN): The modulated signal is transmitted through a communication channel, which may introduce various impairments:
- Rayleigh Fading: This occurs due to multipath propagation, where the transmitted signal reflects off various objects and surfaces before reaching the receiver. These reflections can cause interference, leading to fluctuations in signal strength and quality. Rayleigh fading is particularly significant in mobile communications and environments with many reflective surfaces.
- AWGN (Additive White Gaussian Noise): This is random noise that adds to the signal during transmission. AWGN is characterized by its white (uniform across frequencies) and Gaussian (normal distribution) nature. It affects the signal by introducing randomness and reducing the signal-to-noise ratio (SNR), which can degrade the quality of the received signal.
- Rayleigh Fading: This occurs due to multipath propagation, where the transmitted signal reflects off various objects and surfaces before reaching the receiver. These reflections can cause interference, leading to fluctuations in signal strength and quality. Rayleigh fading is particularly significant in mobile communications and environments with many reflective surfaces.
- Received Signal: After passing through the channel, the signal received by the receiver is a combination of the original modulated signal, Rayleigh fading effects, and AWGN. This signal may be distorted and weakened compared to the original transmitted signal, making it necessary to apply further processing to recover the original message.
Bit error rate due to Rayleigh fading and AWGN noise is...0.16Where is the bit error rate due to only AWGN noise is 0.078 (for BPSK modulation at 0 dB SNR) - Equalization: To address the distortions caused by Rayleigh fading and other channel impairments, equalization techniques are used. Equalization aims to reverse the effects of distortion and restore the signal to its intended form. It involves adjusting the signal to compensate for the channel’s impairments and improve the overall quality and reliability of the received signal. Various equalization techniques include linear equalizers, decision feedback equalizers, and adaptive equalizers.
- Demodulation: Once the signal has been equalized, demodulation is performed to extract the original message signal from the modulated carrier signal. Demodulation reverses the modulation process, removing the carrier signal and recovering the original data. This stage is critical for retrieving the information that was transmitted over the communication channel.
- Message Signal Recovery: After demodulation, the original message signal is recovered. This stage represents the successful completion of the communication process, where the transmitted data is accurately retrieved and can be used by the receiver. The quality of the recovered message signal depends on the effectiveness of the modulation, channel equalization, and demodulation processes.
