In a previous post we had discussed MIMO capacity in a fading environment and compared it to AWGN capacity. It sometimes feels unintuitive that fading capacity can be higher than AWGN capacity. If a signal is continuously fluctuating how is it possible that we are able to have reliable communication. But this is the remarkable feature of MIMO systems that they are able to achieve blazing speeds over an unreliable channel, at least theoretically. It has been shown mathematically that an NxN MIMO channel is equivalent to N SISO channels in parallel.

Continue reading MIMO, SIMO and MISO Capacity in AWGN and Fading Environment# Category Archives: Antennas

# Fundamentals of Direction of Arrival Estimation

Direction of Arrival (DOA) estimation is a fundamental problem in communications and signal processing with application in cellular communications, radar, sonar etc. It has become increasingly important in recent times as 5G communications uses DOA to spatially separate the users resulting in higher capacity and throughput. Direction of Arrival estimation can be thought of as the converse of beamforming. As you might recall from the discussion in previous posts, in beamforming you use the steering vector to receive a signal from a particular direction, rejecting the signals from other directions. In DOA estimation you scan the entire angular domain to find the required signal or signals and estimate their angles of arrival and possibly the ranges as well.

Continue reading Fundamentals of Direction of Arrival Estimation# Near Field of an Antenna

The Electromagnetic Radiation from an antenna, particularly dipole antenna, has been studied in great detail. The mathematical framework proposed by Maxwell has stood the test of time and theoretical concepts have been verified through physical measurements. But the behavior of Electromagnetic (EM) waves close to the radiating antenna is not that well understood. This region that extends to about a wavelength from the antenna is called Near Field, as opposed to Far Field, which extends further out. The Near Field is further divided into Reactive Near Field and Radiative Near Field.

Continue reading Near Field of an Antenna# Reconfigurable Intelligent Surfaces Explained

Wireless channel is inherently unpredictable and this results in loss of information as it travels from the transmitter to the receiver. The main reason for this is that multiple copies of the wireless signal arrive at the receiver which sometimes add constructively and at other times destructively, causing deep fades. The deciding factor between signal copies (think of them as echoes) adding constructively or destructively is the relative phase. If the phases are aligned the signals add up but if the phases are not aligned, we get a fade (fades can be as deep as 60-80dB). Wireless engineers over the years have worked around this problem by using multiple antennas also called antenna arrays.

Continue reading Reconfigurable Intelligent Surfaces Explained# Massive MIMO and Antenna Correlation

Some Background

In a previous post we calculated the Bit Error Rate (BER) of a Massive MIMO system using two different channel models namely deterministic and probabilistic. The deterministic channel model is derived from the geometry of the array (ULA in this case) and the distribution of users in the cell. Whereas probabilistic channel model assumes that the channel is flat fading and can be modeled, between each transmit receive pair, as a complex, circularly symmetric, Gaussian random variable with mean of zero and variance of 0.5 per dimension.

Continue reading Massive MIMO and Antenna Correlation# Fundamentals of a Circular Array – Mathematical Model and Code

###### Array Factor and Element Factor

In the previous post we discussed the case of a Square Array which is a special case of a Rectangular Array. The code we shared can handle both the cases as well as Uniform Linear Array. We did briefly talk about the response of an element vs the response of an array, but we did not put forward the mathematical relationship. So here it is:

Response of an Array = Array Factor x Element Factor

In this post as well as previous posts we have assumed the element response to be isotropic (or at least omni-directional in the plane of the array) giving us an Element Factor of 1. So the array response is nothing but equal to the Array Factor. In this post we mostly discuss the 2D Array Factor but briefly touch upon the 3D case well at the end. Continue reading Fundamentals of a Circular Array – Mathematical Model and Code