The term 'MIMO' was originally applied to systems with multiple antennas on both the transmitter (Tx) and receiver (Rx) sides. MIMO is a key component of Wi-Fi 4 and 5, 3G, and 4G cellular networks. This method was introduced to increase the capacity of a channel by sending multiple simultaneous data streams through a single channel. All simultaneous data streams in a MIMO system are encoded orthogonally multiplexed, which reduces interference. Massive MIMO is used extensively in 5G to achieve extremely high capacity and to communicate via * beamforming* or directional transmission.

## 1. Some essential characteristics of a MIMO system

## 1.1. Spatial Division Multiplexing Access (SDMA)

SDMA is a key feature of MIMO, allowing a base station (BS) to communicate with several devices simultaneously (or even using the same frequency) if they are in different locations. There may be no knowledge of channel information at the transmitter.

## 1.2. Spatial Multiplexing

Another essential feature of MIMO systems is spatial multiplexing. The singular value decomposition of the channel matrix is used to create independent data streams. We assign power to these separate paths using the eigenvalue matrix in this technique.

One of SDMA's difficulties is solved here. Assume two devices are connected to BS in the case of spatial division multiplexing. Now, BS will be perplexed to decide how much power will be utilized by each user; on the other hand, BS can transmit similar power to those mobile devices that are positioned at 6 meters and 100 meters apart, accordingly from the BS station. There is power wastage since a user's device positioned 6 meters away can connect with BS without consuming as much power as a user's device positioned 100 meters away. Because the transmitter has some channel information, this problem is overcome using the spatial multiplexing technique.

## 2. Mathematical representation of a MIMO system

**+ n**

Here,** y **is the received signal vector

** H **denotes the channel matrix

** n **denotes the noise vector

## 3. Capacity of a MIMO system

First, we try to calculate channel information using SVD, **H=U**∑**V ^{H}**

The channel matrix is divided in this way: **U** and **V** are unitary matrices and ∑ diagonal eigenvalue matrices with decreasing order of components. It assists us in allocating the necessary power to each eigen path. Each diagonal eigenmatrix element is responsible for an independent path between the transmitter and receiver. Shortly, we'll write a separate article about SVD.

For now, the system’s capacity is,

**C = log _{2} det(1 + ρ*HQH^{H}) **bits/s/Hz

Where, **Q = VSV ^{H}**

**S = **diagonal matrix derived after allocating power to the diagonal matrix ∑ above.

## Benefits of Massive MIMO

**1. Improved coverage at cell edge:**

**2. Improved throughput**

**3. It enables brand new Millimeter Wave Band**

#beamforming # mimo beamforming