Skip to main content

Massive MIMO | SVD, Multiplexing, Rank and Condition Number

 

Today, we'll talk about the importance of massive MIMO in modern 5G communication systems. We are aware that MIMO technology has been used in the past for 4G LTE. Massive MIMO has a number of advantages over traditional MIMO systems. Now I'll go over some of the basic benefits of a basic MIMO setup against a single transmitter and receiver antenna. 1. MIMO is a technology that allows for spatial multiplexing; 2. We can transmit the same signal from numerous antennas in a MIMO system for higher beamforming gain; 3. Allows for space, frequency, and time diversity.


Singular Value Decomposition (SVD): 

Go through the process of singular value decomposition (SVD)

H = U∑VH  

Mathematically, SVD denotes: 

Here in massive MIMO, we basically factorize the channel matrix, 


where, U and V are unitary matrices
             = diagonal singular value matrix


The values of the unitary matrices U and V are arranged in such a way that the singular values of the matrix ∑ are in decreasing order. SVD aids in the optimal allocation of power to each singular value. It also has something to do with spatial multiplexing. In an upcoming essay, we'll go over SVD in greater depth.


Spatial Multiplexing (SM):

Spatial multiplexing allows us to deliver multiple data streams to the transmitter and receiver at the same time. The number of simultaneous and independent data streams between TX and RX is determined by the singular values in matrix ∑ above. The number of simultaneous data streams is determined by the rank of a wireless communication channel matrix. In MIMO communication, capacity of the system increases with the number of antenna elements and the log of the signal to noise ratio, or SNR.


Signal Coherency at receiver side:

Now I'll talk about how we can go from simple MIMO to massive MIMO for 5G connectivity. We already know that increasing the antenna array size in MIMO improves spectral efficiency. When the number of antenna elements in a huge MIMO system is increased, however, the signal phase alignment at the receiver side improves. It basically focuses the resulting strong signal (which is formed by the same signal delivered by many closely spaced antenna elements) in a single direction.


Massive MIMO communication – Uplink and Downlink

Users directly transmit their symbols via the large MIMO UL link. To reduce interference in one's transmitted symbol from symbols of other users, the BS must recover each individual's symbol using linear decoding. We employ a pre-coding (beamforming) technique for downlink or DL communication to cancel interference between users using correct baseband and RF pre-coding and a combining (or weighting) matrix.


Rank and Condition number of a massive MIMO channel matrix while using with millimeter wave band 

The number of independent rows or columns in a matrix determines its rank. When we determine the rank of a channel matrix, we may determine how many independent data streams are possible between the TX and RX MIMO antennas. In most circumstances, the rank of a channel matrix in massive MIMO is very small, especially when operating at extremely high frequencies, such as the millimetre wave band. As a result, it generates a sparse channel matrix.

The condition number is a statistic used to characterise the quality of MIMO channels. It is defined as the ratio of the greatest to lowest singular value in the singular value decomposition of a matrix. In MIMO, a low condition number (below 20 dB) usually indicates good orthogonality between sub-channels. However, the condition number is substantially higher (worse) here during extremely high frequency operation. As a result, we employ beamforming to overcome the aforementioned constraints. 


#beamforming



People are good at skipping over material they already know!

View Related Topics to







Contact Us

Name

Email *

Message *

Popular Posts

Simulation of ASK, FSK, and PSK using MATLAB Simulink (with Online Simulator)

📘 Overview 🧮 How to use MATLAB Simulink 🧮 Simulation of ASK using MATLAB Simulink 🧮 Simulation of FSK using MATLAB Simulink 🧮 Simulation of PSK using MATLAB Simulink 🧮 Simulator for ASK, FSK, and PSK 🧮 Digital Signal Processing Simulator 📚 Further Reading ASK, FSK & PSK HomePage MATLAB Simulation Simulation of Amplitude Shift Keying (ASK) using MATLAB Simulink In Simulink, we pick different components/elements from MATLAB Simulink Library. Then we connect the components and perform a particular operation. Result A sine wave source, a pulse generator, a product block, a mux, and a scope are shown in the diagram above. The pulse generator generates the '1' and '0' bit sequences. Sine wave sources produce a specific amplitude and frequency. The scope displays the modulated signal as well as the original bit sequence created by the pulse generator. Mux i...

MATLAB Codes for Various types of beamforming | Beam Steering, Digital...

📘 How Beamforming Improves SNR 🧮 MATLAB Code 📚 Further Reading 📂 Other Topics on Beamforming in MATLAB ... MIMO / Massive MIMO Beamforming Techniques Beamforming Techniques MATLAB Codes for Beamforming... How Beamforming Improves SNR The mathematical [↗] and theoretical aspects of beamforming [↗] have already been covered. We'll talk about coding in MATLAB in this tutorial so that you may generate results for different beamforming approaches. Let's go right to the content of the article. In analog beamforming, certain codebooks are employed on the TX and RX sides to select the best beam pairs. Because of their beamforming gains, communication created through the strongest beams from both the TX and RX side enhances spectrum efficiency. Additionally, beamforming gain directly impacts SNR improvement. Wireless communication system capacity = bandwidth*log2(1+SNR)...

Theoretical BER vs SNR for binary ASK, FSK, and PSK with MATLAB Code + Simulator

📘 Overview & Theory 🧮 MATLAB Codes 📚 Further Reading Theoretical BER vs SNR for Amplitude Shift Keying (ASK) The theoretical Bit Error Rate (BER) for binary ASK depends on how binary bits are mapped to signal amplitudes. For typical cases: If bits are mapped to 1 and -1, the BER is: BER = Q(√(2 × SNR)) If bits are mapped to 0 and 1, the BER becomes: BER = Q(√(SNR / 2)) Where: Q(x) is the Q-function: Q(x) = 0.5 × erfc(x / √2) SNR : Signal-to-Noise Ratio N₀ : Noise Power Spectral Density Understanding the Q-Function and BER for ASK Bit '0' transmits noise only Bit '1' transmits signal (1 + noise) Receiver decision threshold is 0.5 BER is given by: P b = Q(0.5 / σ) , where σ = √(N₀ / 2) Using SNR = (0.5)² / N₀, we get: BER = Q(√(SNR / 2)) Theoretical BER vs ...

Online Simulator for ASK, FSK, and PSK

Try our new Digital Signal Processing Simulator!   •   Interactive ASK, FSK, and BPSK tools updated for 2025. Start Now Interactive Modulation Simulators Visualize binary modulation techniques (ASK, FSK, BPSK) in real-time with adjustable carrier and sampling parameters. 📡 ASK Simulator 📶 FSK Simulator 🎚️ BPSK Simulator 📚 More Topics ASK Modulator FSK Modulator BPSK Modulator More Topics Simulator for Binary ASK Modulation Digital Message Bits Carrier Freq (Hz) Sampling Rate (...

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

Bit Error Rate (BER) & SNR Guide Analyze communication system performance with our interactive simulators and MATLAB tools. 📘 Theory 🧮 Simulators 💻 MATLAB Code 📚 Resources BER Definition SNR Formula BER Calculator MATLAB Comparison 📂 Explore M-ary QAM, PSK, and QPSK Topics ▼ 🧮 Constellation Simulator: M-ary QAM 🧮 Constellation Simulator: M-ary PSK 🧮 BER calculation for ASK, FSK, and PSK 🧮 Approaches to BER vs SNR What is Bit Error Rate (BER)? The BER indicates how many corrupted bits are received compared to the total number of bits sent. It is the primary figure of merit for a...

Constellation Diagrams of ASK, PSK, and FSK (with MATLAB Code + Simulator)

Constellation Diagrams: ASK, FSK, and PSK Comprehensive guide to signal space representation, including interactive simulators and MATLAB implementations. 📘 Overview 🧮 Simulator ⚖️ Theory 📚 Resources Definitions Constellation Tool Key Points MATLAB Code 📂 Other Topics: M-ary PSK & QAM Diagrams ▼ 🧮 Simulator for M-ary PSK Constellation 🧮 Simulator for M-ary QAM Constellation 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 on...

Power Spectral Density Calculation Using FFT in MATLAB

📘 Overview 🧮 Steps to calculate the PSD of a signal 🧮 MATLAB Codes 📚 Further Reading Power spectral density (PSD) tells us how the power of a signal is distributed across different frequency components, whereas Fourier Magnitude gives you the amplitude (or strength) of each frequency component in the signal. Steps to calculate the PSD of a signal Firstly, calculate the fast Fourier transform (FFT) of a signal. Then, calculate the Fourier magnitude (absolute value) of the signal. Square the Fourier magnitude to get the power spectrum. To calculate the Power Spectral Density (PSD), divide the squared magnitude by the product of the sampling frequency (fs) and the total number of samples (N). Formula: PSD = |FFT|^2 / (fs * N) Sampling frequency (fs): The rate at which the continuous-time signal is sampled (in ...

MATLAB Code for ASK, FSK, and PSK (with Online Simulator)

MATLAB Code for ASK, FSK, and PSK Comprehensive implementation of digital modulation and demodulation techniques with simulation results. 📘 Theory 📡 ASK Code 📶 FSK Code 🎚️ PSK Code 🕹️ Simulator 📚 Further Reading Amplitude Shift Frequency Shift Phase Shift Live Simulator ASK, FSK & PSK HomePage MATLAB Code MATLAB Code for ASK Modulation and Demodulation COPY % The code is written by SalimWireless.Com clc; clear all; close all; % Parameters Tb = 1; fc = 10; N_bits = 10; Fs = 100 * fc; Ts = 1/Fs; samples_per_bit = Fs * Tb; rng(10); binar...