Skip to main content

Menu

Home 📘 Wireless Communication (Main Page) Constellation Diagrams BER vs SNR GMSK MSK Channel Impulse Response Modulation Schemes MIMO Technology OFDM MATLAB Projects Contact
Login Try App

Mathematical Aspects of Beamforming in MIMO



Beam steering, which permits strong directed beams towards the receiver to combat excessive pathloss, especially for higher frequency bands, immediately comes to mind when discussing mathematical aspects of Beamforming in MIMO antennas. On the other side, it also lessens signal interference and improves the effectiveness of spatial multiplexing in Massive MIMO communication. Let's go right to the mathematical parts of Beamforming, which will make it easier for you to code in Python and MATLAB.



1. Beam Steering (Analog Beamforming)




In the first stage, the BS applies beam steering at the side of the mobile station (MS) while the MS enables omnidirectional transmission. In the following step, the MS uses beam steering while the BS is an omnidirectional transmitter. The best beamformer and combiner pair are then identified at BS & MS, and they make communication available. Following is an outline of the codebook:


 

 
Let's say a small town or village has a cell tower in the midst of it. Now everybody can understand the cell tower's 360-degree coverage area (if not, you restrict the coverage to a particular direction or sector). The codebook above specifies what the signal intensity will be different at a specific coverage zone defined by the azimuth angle or elevation angular ranges from the transmitter (here, cell tower).

Assume that the first element in the given set, f, indicates the coverage zone from 0 to 10 degrees.
The second element depicts the coverage area between 10 and 20 degrees from the base station.
Additionally, every component in the codebook has directions, or azimuth angle ranges from 0 to 360 degree.
A similar procedure is applicable for mobile stations (MS) to identify the strongest beam between them by determining the optimum path (here, beam) from MS to BS.


2. Digital Beamforming


Fig: Digital Beamforming

Each antenna element, in this case, is connected to a separate RF chain during digital Beamforming. Filters, mixers, amplifiers, etc., make up RF chains. Each RF chain controls a particular data stream between TX and RX.
Any signal or data stream transmitted by transmitter side antenna T1 is typically received by all receiver side antennas. There are four different user equipment (UEs) or mobile stations shown in the above diagram. All four UEs receive any signal that is sent by antenna T1. Assume that receiver R1 was the only one for which the signal was intended. It will then be regarded as interference for receiver side antennas R1, R2, R3,..., and R8. In this situation, a digital beamforming matrix is crucial to eliminate interference at all undesirable receivers while transmitting the signal from T1. and permit R1 to only receive the signal. The individual data streams between T2 and R2, T3 and R3, and so forth can be assumed similarly.

At the receiver side, the signal received by users vector y, 
                                                                y = √ρHDs + n
                                                               where H=Channel Matrix
                                                               s = transmitted symbol/signal
                                                               n = additive white Gaussian noise (AWGN)
                                                               ρ = average received power
                                                               D = digital precoding/beamforming matrix

For a multiuser scenario, the hybrid beamforming equation looks like
                                                               y = √ρ.H.[D1 D2 ... Dn].s + n
                                                               Where 'Dn' denotes the digital precoder 
                                                                for u-th user

Now cancel interference at u-th user due to other users; we must design the baseband precoder so that HuDn for nǂ u should be zero at the u-th mobile station (MS). Therefore, HuDn =0 cancels interferences at u-th MS.
 
 
 ------------------------------------------------------------------------------------------------------------
. - - -  - - - - - - beamforming
                            - -  - Analog Beamforming
.                           - -  - Digital Beamforming
.                                      - - Equations related to Spectral Efficiency in Digital Beamforming
.                           - -  - Hybrid Beamforming
.                                      - - Equations related to Spectral Efficiency in Hybrid Beamforming
--------------------------------------------------------------------------------------------------------------

3. Hybrid Beamforming


First, we connect multiple antenna elements in hybrid Beamforming to increase gain, which is crucial for today's higher-frequency wireless communication systems. Then, precisely as illustrated in the above figure, we apply digital Beamforming to those RF chains. The key advantages of hybrid Beamforming are that
Less interference than digital Beamforming without sacrificing a significant difference in a MIMO system's throughput.
The transmitted signal has a large amount of gain added by analog Beamforming or beam steering to extend its range.
For lower-dimensional MIMO systems, digital Beamforming works well, but massive MIMO systems are where the future of communication is headed. Compared to digital Beamforming, hybrid Beamforming is less complicated and more cost-effective.

 

Further Reading

People are good at skipping over material they already know!

View Related Topics to







Contact Us

Name

Email *

Message *

Popular Posts

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 📚 Further Reading 📂 View Other Topics on M-ary QAM, M-ary PSK, QPSK ... 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR What is Bit Error Rate (BER)? The abbreviation BER stands for Bit Error Rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. BER = (number of bits received in error) / (total number of tran...
Read more

Constellation Diagrams of ASK, PSK, and FSK

📘 Overview of Energy per Bit (Eb / N0) 🧮 Online Simulator for constellation diagrams of ASK, FSK, and PSK 🧮 Theory behind Constellation Diagrams of ASK, FSK, and PSK 🧮 MATLAB Codes for Constellation Diagrams of ASK, FSK, and PSK 📚 Further Reading 📂 Other Topics on Constellation Diagrams of ASK, PSK, and FSK ... 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM BASK (Binary ASK) Modulation: Transmits one of two signals: 0 or -√Eb, where Eb​ is the energy per bit. These signals represent binary 0 and 1.    BFSK (Binary FSK) Modulation: Transmits one of two signals: +√Eb​ ( On the y-axis, the phase shift of 90 degrees with respect to the x-axis, which is also termed phase offset ) or √Eb (on x-axis), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  BPSK (Binary PSK) Modulation: Transmits one of two signals...
Read more

Theoretical vs. simulated BER vs. SNR for ASK, FSK, and PSK

📘 Overview 🧮 Simulator for calculating BER 🧮 MATLAB Codes for calculating theoretical BER 🧮 MATLAB Codes for calculating simulated BER 📚 Further Reading BER vs. SNR denotes how many bits in error are received for a given signal-to-noise ratio, typically measured in dB. Common noise types in wireless systems: 1. Additive White Gaussian Noise (AWGN) 2. Rayleigh Fading AWGN adds random noise; Rayleigh fading attenuates the signal variably. A good SNR helps reduce these effects. Simulator for calculating BER vs SNR for binary ASK, FSK, and PSK Calculate BER for Binary ASK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary FSK Modulation Enter SNR (dB): Calculate BER Calculate BER for Binary PSK Modulation Enter SNR (dB): Calculate BER BER vs. SNR Curves MATLAB Code for Theoretical BER % The code is written by SalimWireless.Com clc; clear; close all; % SNR va...
Read more

MATLAB Code for ASK, FSK, and PSK

📘 Overview & Theory 🧮 MATLAB Code for ASK 🧮 MATLAB Code for FSK 🧮 MATLAB Code for PSK 🧮 Simulator for binary ASK, FSK, and PSK Modulations 📚 Further Reading ASK, FSK & PSK HomePage MATLAB Code MATLAB Code for ASK Modulation and Demodulation % The code is written by SalimWireless.Com % Clear previous data and plots clc; clear all; close all; % Parameters Tb = 1; % Bit duration (s) fc = 10; % Carrier frequency (Hz) N_bits = 10; % Number of bits Fs = 100 * fc; % Sampling frequency (ensure at least 2*fc, more for better representation) Ts = 1/Fs; % Sampling interval samples_per_bit = Fs * Tb; % Number of samples per bit duration % Generate random binary data rng(10); % Set random seed for reproducibility binary_data = randi([0, 1], 1, N_bits); % Generate random binary data (0 or 1) % Initialize arrays for continuous signals t_overall = 0:Ts:(N_bits...
Read more

MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...

🧮 MATLAB Code for BPSK, M-ary PSK, and M-ary QAM Together 🧮 MATLAB Code for M-ary QAM 🧮 MATLAB Code for M-ary PSK 📚 Further Reading MATLAB Script for BER vs. SNR for M-QAM, M-PSK, QPSK, BPSK % Written by Salim Wireless clc; clear; close all; num_symbols = 1e5; snr_db = -20:2:20; psk_orders = [2, 4, 8, 16, 32]; qam_orders = [4, 16, 64, 256]; ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); for i = 1:length(psk_orders) psk_order = psk_orders(i); for j = 1:length(snr_db) data_symbols = randi([0, psk_order-1], 1, num_symbols); modulated_signal = pskmod(data_symbols, psk_order, pi/psk_order); received_signal = awgn(modulated_signal, snr_db(j), 'measured'); demodulated_symbols = pskdemod(received_signal, psk_order, pi/psk_order); ber_psk_results(i, j) = sum(data_symbols ~= demodulated_symbols) / num_symbols; end end for i...
Read more

Comparisons among ASK, PSK, and FSK | And the definitions of each

📘 Comparisons among ASK, FSK, and PSK 🧮 Online Simulator for calculating Bandwidth of ASK, FSK, and PSK 🧮 MATLAB Code for BER vs. SNR Analysis of ASK, FSK, and PSK 📚 Further Reading 📂 View Other Topics on Comparisons among ASK, PSK, and FSK ... 🧮 Comparisons of Noise Sensitivity, Bandwidth, Complexity, etc. 🧮 MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK 🧮 Online Simulator for ASK, FSK, and PSK Generation 🧮 Online Simulator for ASK, FSK, and PSK Constellation 🧮 Some Questions and Answers Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK    Comparisons among ASK, PSK, and FSK Comparison among ASK, FSK, and PSK Parameters ASK FSK PSK Variable Characteristics Amplitude Frequency ...
Read more

Calculation of SNR from FFT bins in MATLAB

📘 Overview 🧮 MATLAB Code for Estimation of SNR from FFT bins of a Noisy Signal 🧮 MATLAB Code for Estimation of Signal-to-Noise Ratio from Power Spectral Density Using FFT and Kaiser Window Periodogram from real signal data 📚 Further Reading   Here, you can find the SNR of a received signal from periodogram / FFT bins using the Kaiser operator. The beta (β) parameter characterizes the Kaiser window, which controls the trade-off between the main lobe width and the side lobe level in the frequency domain. For that you should know the sampling rate of the signal.  The Kaiser window is a type of window function commonly used in signal processing, particularly for designing finite impulse response (FIR) filters and performing spectral analysis. It is a general-purpose window that allows for control over the trade-off between the main lobe width (frequency resolution) and side lobe levels (suppression of spectral leakage). The Kaiser window is defined...
Read more

Theoretical BER vs SNR for BPSK

Theoretical Bit Error Rate (BER) vs Signal-to-Noise Ratio (SNR) for BPSK in AWGN Channel Let’s simplify the explanation for the theoretical Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) for Binary Phase Shift Keying (BPSK) in an Additive White Gaussian Noise (AWGN) channel. Key Points Fig. 1: Constellation Diagrams of BASK, BFSK, and BPSK [↗] BPSK Modulation Transmits one of two signals: +√Eb or −√Eb , where Eb is the energy per bit. These signals represent binary 0 and 1 . AWGN Channel The channel adds Gaussian noise with zero mean and variance N₀/2 (where N₀ is the noise power spectral density). Receiver Decision The receiver decides if the received signal is closer to +√Eb (for bit 0) or −√Eb (for bit 1) . Bit Error Rat...
Read more