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

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...

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 (...

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 ...

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 one ...

UGC NET Electronic Science Previous Year Question Papers

Home / Engineering & Other Exams / UGC NET 2022 PYQ 📥 Download UGC NET Electronics PDFs Complete collection of previous year question papers, answer keys and explanations for Subject Code 88. Start Downloading UGC-NET (Electronics Science, Subject code: 88) Subject_Code : 88; Department : Electronic Science; 📂 View All Question Papers UGC Net Electronic Science Question Paper With Answer Key Download Pdf [June 2025] with full explanation UGC Net Electronic Science Question Paper With Answer Key Download Pdf [December 2024] UGC Net Paper 1 With Answer Key Download Pdf [Sep 2024] with full explanation UGC Net Electronic Science Question Paper With Answer Key Download Pdf [Aug 2024] with full explanation UGC Net Paper 1 With Answer Key Download...

FM Modulation Online Simulator

Frequency Modulation Simulator Message Frequency (fm): Hz Carrier Frequency (fc): Hz Carrier Amplitude (Ac): Modulation Index (β): Frequency deviation Δf = β × fm Online Signal Processing Simulations Home Page >

Theoretical vs. simulated BER vs. SNR for ASK, FSK, and PSK (MATLAB Code + Simulator)

📘 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...

ASK, FSK, and PSK (with MATLAB + Online Simulator)

📘 ASK Theory 📘 FSK Theory 📘 PSK Theory 📊 Comparison 🧮 MATLAB Codes 🎮 Simulator ASK or OFF ON Keying ASK is a simple (less complex) Digital Modulation Scheme where we vary the modulation signal's amplitude or voltage by the message signal's amplitude or voltage. We select two levels (two different voltage levels) for transmitting modulated message signals. Example: "+5 Volt" (upper level) and "0 Volt" (lower level). To transmit binary bit "1", the transmitter sends "+5 Volts", and for bit "0", it sends no power. The receiver uses filters to detect whether a binary "1" or "0" was transmitted. Fig 1: Output of ASK, FSK, and PSK modulation using MATLAB for a data stream "1 1 0 0 1 0 1 0" ( Get MATLAB Code ) ...