I would like to solve beamforming weight in a C-RAN environment for a reinforcement learning task. I have studied different beamforming weigh calculations such as Capon and MUISC. But, I still can not understand the concept thoroughly. I want to implement it in python. Consider the following scenario:
We have two RRHs and four receivers. Receivers 1 and 2 are associated with RRH1 and receiver 3 and 4 is associate with RRH2.
My understanding is as follow. First, we should use the direction of arrival (DoA) between RRH1 and recv1 to compute weights for recev1. let call the calculated weights as w11(RRH1, recv1). We then calculate w12(RRH1, recv2), w23(cRRH2, recv3), and w24(RRH2, recv4) using corresponding DoAs.
Next, we use following formula to calculate SINR at each receiver location:
SINR1=(h11*w11)/(h21*w11+𝜎2)
SINR2=(h12*w12)/(h22*w12+𝜎2)
SINR3=(h23*w23)/(h13*w23+𝜎2)
SINR4=(h24*w24)/(h14*w24+𝜎2)
by hij, I mean the received signal from RRH i at receiver location j.
Would you let me know if my understating of the concept is ok?
Beamforming improves the SNIR (Signal-to-Noise and Interference Ratio) by attenuating unwanted noise and interference while amplifying the desired signal. Here's how to calculate SNIR in the presence of beamforming:
Here's a Python code example for calculating SNIR after beamforming:
Python
import numpy as np def calculate_snir(signal_power, noise_psd, beamforming_gain): """ Calculates the Signal-to-Noise Ratio (SNIR) after beamforming. Args: signal_power: Power of the desired signal (float). noise_psd: Noise power spectral density (array-like). beamforming_gain: Beamforming gain in the direction of the signal (float). Returns: The calculated SNIR in dB. """ # Integrate noise power over the bandwidth noise_power = np.sum(noise_psd) # Apply beamforming gain enhanced_signal_power = signal_power * beamforming_gain # Calculate SNIR in linear scale snr_linear = enhanced_signal_power / noise_power # Convert SNIR to dB snir_db = 10 * np.log10(snr_linear) return snir_db # Example usage (assuming values are pre-calculated) signal_power = 1e-3 # Watts noise_psd = np.ones(100) * 1e-9 # Noise PSD (Watts/Hz) beamforming_gain = 10 # Linear gain snir_db = calculate_snir(signal_power, noise_psd, beamforming_gain) print(f"SNIR after beamforming: {snir_db:.2f} dB")
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