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Massive MIMO | SVD, Multiplexing, Rank and Condition Number

 

Today, we'll talk about the importance of large MIMO in modern 5G communication systems. We are aware that the 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 better signal correlation; 3. Allows for space, frequency, and time diversion.


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 matix
            ∑ = diagonal eigen value matrix


The values of the unitary matrices U and V are arranged in such a way that the eigen values of the matrix ∑ are in decreasing order. SVD aids in the optimal allocation of power to each Eigen 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 eigen values in eigen matrix ∑ above. The number of simultaneous data streams is determined by the rank of a wireless communication channel matrix when channel matrix, H is sparse. In MIMO communication, capacity of system is proportional to the number of antenna elements and the signal to noise ratio, or SNR.


Signal Correlation 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 correlation 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 / processing. To reduce interference in one's transmitted symbol from symbols of other users, BS must recover each individual's symbol using basic linear decoding. We employ a pre-coding (beam forming) technique for downlink or DL communication to cancel interferences 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 in wireless communications. 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 worse here during extremely high frequency operation. As a result, we employ beamforming to overcome the aforementioned constraints. 

#beamforming

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