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.

Basic benefits:
1. MIMO is a technology that allows for spatial multiplexing;
2. Higher beamforming gain via numerous antennas;
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,

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.

Master Massive MIMO Technology

Explore our comprehensive simulator and deep-dive technical guides for 5G Beamforming.

Launch Simulator >

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 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

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 the millimetre wave band. As a result, it generates a sparse channel matrix.

% Example Matlab Rank Calculation
H = [1 0.5; 0.5 1];
rank_H = rank(H);
cond_H = cond(H);
disp(['Rank: ', num2str(rank_H)]);

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 MIMO, a low condition number (below 20 dB) usually indicates good orthogonality. However, the condition number is substantially higher here during extremely high frequency operation. As a result, we employ beamforming to overcome constraints.

Read more about Rank and Condition number

#beamforming

People are good at skipping over material they already know!

View Related Topics to







Contact Us

Name

Email *

Message *

Popular Posts

How to use MATLAB Simulink

Introduction to MATLAB Simulink MATLAB Simulink is a popular add-on of MATLAB. Here, you can use different blocks like modulator, demodulator, AWGN channel, etc. And you can do experiments on your own. Steps to Get Started 1. Go to the 'Simulink' tab at the top navbar of MATLAB. If not found, click on the add-on tab, search 'Simulink,' and then click on it to add. 2. Once you installed the simulation, click the 'new' tap at the top left corner. 3. Then, search the required blocks in the 'Simulink library.' Then, drag it to the editor space. 4. You can double-click on the blocks to see the input parameters. 5. Then, connect the blocks by dragging a line from one block's output terminal to another block's input. 6. If the connection is complete, click the 'run' tab in the middle of the top navbar. 7. After clicking on the run ...

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...

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

📘 Overview 🧮 Simulator 💻 Theoretical Code 📊 Simulated Code 📚 Resources Overview 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. Bit Error Rate (BER) Equations BER formulas for ASK, FSK, and PSK modulation schemes. ASK BER = 0.5 × erfc(0.5 × √SNR) FSK BER = 0.5 × erfc(√(SNR / 2)) PSK BER = 0.5 × erfc(√SNR) erfc / Q-function (Click here) Live BER S...

Rayleigh vs Rician Fading (with MATLAB + Simulator)

  In Rayleigh fading , the channel coefficients tend to have a Rayleigh distribution, which is characterized by a random phase and magnitude with an exponential distribution. This means the magnitude of the channel coefficient follows an exponential distribution with a mean of 1. In Rician fading , there is a dominant line-of-sight component in addition to the scattered components. The channel coefficients in Rician fading can indeed tend towards 1, especially when the line-of-sight component is strong. When the line-of-sight component dominates, the Rician fading channel behaves more deterministically, and the channel coefficients may tend towards the value of the line-of-sight component, which could be close to 1.   MATLAB Script clc; clear all; close all; % Define parameters numSamples = 1000; % Number of samples K_factor = 5; % K-factor for Rician fading SNR_dB = 20; % Signal-to-noise ratio (in dB) % Generate complex Gaussian random variable for Rayleigh fading channel h_r...

UGC-NET Electronic Science Question Paper With Answer Key and Full Explanation [Dec 2023]

    UGC-NET Electronic Science Question Paper With Answer Key Download Pdf [Dec 2023] Download Question Paper               See Answers   2025 | 2024 | 2023 | 2022 | 2021 | 2020 UGC-NET Electronic Science  2023 Answers with Explanations 51. (A): The stacking fault is the most common area defect found in silicon. These faults typically occur along the 111 plane. In the crystalline structure of silicon, atoms are arranged in a specific pattern known as a diamond lattice. A stacking fault refers to a disruption in the normal order of atomic layers within this lattice, which usually occurs in the 111 plane due to the geometric arrangement of the atoms. This type of defect can affect the electrical and mechanical properties of the material, such as the mobility of charge carriers and mechanical strength. 52. (C): The important figure of merit for the microwave application of a Schot...

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...

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 Q. UGC Net Electronic Science Question Paper [June 2025] A. UGC Net Electronic Science Question Paper With Answer Key Download Pdf [June 2025] with full explanation Q. UGC Net Electronic Science Question Paper [December 2024] A. UGC Net Electronic Science Question Paper With Answer Key Download Pdf [December 2024] Q. UGC Net Electronic Science Question Paper [Aug 2024] A. UGC Net Electronic Scien...

OFDM Waveform with MATLAB Code (with Simulator)

  In OFDM (Orthogonal Frequency Division Multiplexing) , we transmit multiple orthogonal subcarriers simultaneously. Since the subcarriers are orthogonal , they do not interfere with each other, which is one of the main advantages of OFDM. Practically, OFDM converts a wideband signal into multiple narrowband orthogonal subcarriers. For typical wireless communication, if the signal bandwidth (or symbol duration) exceeds the coherence bandwidth of the channel, the signal experiences frequency-selective fading . Fading distorts the signal, making it difficult to recover the original information. By using OFDM, we transmit the same wideband signal across multiple orthogonal narrowband subcarriers, reducing the effect of fading. For example, if we want to transmit a signal of bandwidth 1024 kHz , we can divide it into N = 8 subcarriers . Each subcarrier is then spaced by: Δf = Total Bandwidth N = 1024 8 kHz...