The Fourier Transform is often used in Communication and Signal Processing to find the spectral content of a time-domain signal. The most common example is that of a sinusoid in the time domain, resulting in a sharply peaked signal in the frequency domain, also known as a delta function. A rectangular pulse in the time domain has a more complicated frequency domain equivalent, a sinc function. A rectangular pulse may be thought of as a combination of many sinusoids, hence its frequency domain equivalent is not that straightforward.

Continue reading Demystifying the Fourier Transform# Category Archives: Fundamentals

# Why is MIMO Fading Capacity Higher than AWGN Capacity

In a previous post we have seen that MIMO fading capacity is much higher than AWGN capacity with multiple antennas. How is this possible? How can randomness added by a fading channel help us? In this post we try to find the reason for this. Letâ€™s assume the following signal model for a Multi Input Multi Output antenna system.

x=Hs+w

Here s is the N_{T} by 1 signal vector, w is the N_{R} by 1 noise vector and H is the N_{R} by N_{T} channel matrix. The received signal vector is represented by x which has dimensions of N_{R} by 1. In expanded form this can be written as (assuming N_{T} =4 and N_{R} =4):

# MIMO, SIMO and MISO Capacity in AWGN and Fading Environment

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# 5G Data Rates and Shannon Capacity

Recently I came across a **post from T-Mobile** in which they claim to have achieved a download speed of 5.6 Gbps over a 100 MHz channel resulting in a Spectral Efficiency of more than 50 bps/Hz. This was achieved in an MU-MIMO configuration with eight connected devices having an aggregate of 16 parallel streams i.e. two parallel streams per device. The channel used for this experiment was the mid-band frequency of 2.5 GHz.

# 5G Rollout in the USA: Long Way to Go

There is a 3 way race for 5G leadership in the US between T-Mobile(+Sprint), Verizon and AT&T. There are competing claims for the number of 5G subscribers, coverage area and download speeds. But let us look where the 5G industry stands today compared to the expectations a few years back. More than 80% of US population lives in urban areas which comprise of 2% of the total land area of about 10 million squared kilometers. That is 80% of the population lives in an area of about 200,000 squared kilometers.

Continue reading 5G Rollout in the USA: Long Way to Go# 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.

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