A trellis for implementing Viterbi algorithm
Wireless/SDR

Maximum Likelihood Sequence Estimation (MLSE Equalizer)

In the discussion on a wireless channel, we saw that an increased amount of Inter-Symbol Interference (ISI) occurs for high data-rate wireless systems that impacts the system performance to a significant extent. The performance of a linear equalizer suffers from spectral nulls. A Decision Feedback Equalizer (DFE) recovers much of the performance losses due to ISI but it is susceptible to error propagation. In 1972, David Forney published a paper titled "Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference" in which he proposed the idea of sequence estimation. For this purpose, there was an implicit assumption

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Channel hardening implies the channel flutucations due to small-scale fading smooth out
Wireless/SDR

On Massive MIMO, Channel Hardening and Favorable Propagation

Imagine an alien race looking at our planet from outside the solar system through a lens of time. They will notice one unmistakable direction. Our pursuit of MORE in everything. This tendency might be ingrained in the fundamental idea of life itself. To live is to grow. While our dreams for faster transportation face mechanical roadblocks from the laws of physics, technologies for faster communication are only bound by the laws of electromagnetics. Ever since we linked digital electronics to information exchange from one point to another without any physical medium, on-demand reception and transmission of data at any place

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A DNA double helix
DSP

The Concept of Frequency

A wireless signal from one device to another travels through the use of electromagnetic waves propagated by an antenna. Electromagnetic waves have different frequencies and one can pick up a specific signal by tuning a radio Rx to a specific frequency. But what is a frequency anyway? Watch the video below for an interesting description of actual time domain samples and how to interpret their frequency domain representation. A Complex Sinusoid Consider a complex number $V$ in an $IQ$-plane. A complex number is defined as a pair of real numbers in $(x,y)$-plane similar to the vectors but with different arithmetic

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Blocks of a simple binary communication system
Wireless/SDR

A Simple Communication System

"The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point." Claude Shannon – A Mathematical Theory of Communication Our main purpose is to transfer digital information – which is a sequence of bits 0’s and 1’s – from one system to another through a communication channel. Let us return for a moment to the concept behind simple digital logic where logic 0 can be assigned to one voltage level while logic 1 to another. Provided the static discipline is followed, all our system electronics has to do is

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Earth lies in the Goldilocks Zone of our solar system
Wireless/SDR

Diversity in Wireless Communication Systems

Diversity is one of those few ideas that are extremely dumb and extremely clever at the same time. It can be explained in one sentence as well as in a whole book. The basic idea, nevertheless, is quite simple. What is Diversity? Consider the following two different cases. Many phenomena in the world need a series of outcomes to succeed. For instance, for life to exist in the cold and dark universe, we need a star to provide energy as heat. A planet is also required as a home. Furthermore, this planet must reside in the Goldilocks Zone of that

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