In the discussion on diversity, we described in detail the idea of space diversity through an example of Selection Combining (SC). Maximum Ratio Combining (MRC) is another space diversity scheme that embodies the concept behind generalized beamforming — the main technology in 5G cellular systems. Let us find out how. Setup Consider a wireless link with 2 Tx antenna and 2 (or more) Rx antennas as shown in the figure below. At each symbol time, a data symbol $s$ is transmitted which belongs to a Quadrature Amplitude Modulation (QAM) scheme. To focus on the events happening within one symbol time

Continue reading# Category: Wireless/SDR

Wireless communications and Software Defined Radio (SDR)

## Least Mean Square (LMS) Equalizer – A Tutorial

The LMS algorithm was first proposed by Bernard Widrow (a professor at Stanford University) and his PhD student Ted Hoff (the architect of the first microprocessor) in the 1960s. Due to its simplicity and robustness, it has been the most widely used adaptive filtering algorithm in real applications. An LMS equalizer in communication system design is just one of those beautiful examples and its other applications include noise and echo cancellation, beamforming, neural networks and so on. Background The wireless channel is a source of severe distortion in the received (Rx) signal and our main task is to remove the

Continue reading## Proof of Poisson Sum Formula

The Poisson sum formula was discovered by the French mathematician and physicist Siméon Denis Poisson. It has several applications in digital signal processing, among which our concern is the periodic summation of modulated pulses in digital communication systems. Assume that $p(t)$ is a pulse shape (or any continuous-time function if you are not familiar with digital communications) and $P(f)$ is its Fourier Transform. The pulse is sampled at a rate of $f_s$ to produce its discrete version $p(nT_s)$ where $T_s=1/f_s$ is the duration between two samples. The Poisson summation formula relates these two quantities as \begin{equation}\label{equation-poisson-sum-formula} \frac{1}{T_s}\sum _{k=-\infty}^{\infty} P\left(f+\frac{k}{T_s}\right) =

Continue reading## Design of a Low-SNR Receiver

Wireless communication is energy inefficient due to the nature of the medium that spreads out energy in an unguided manner, as opposed to guided media like optical fiber and coaxial cable. To avoid wastage of power, one solution is to lower the transmit (Tx) power but then the receiver is left with the herculean task of efficiently demodulating the receive symbols at a low SNR. This article describes the design and implementation of one such receiver. Background The physical layer of a receiver system consists of three major parts, namely the frontend, the inner receiver, and the outer receiver. The

Continue reading## Advantages and Disadvantages of OFDM – A Summary

Orthogonal Frequency Division Multiplexing (OFDM) is a technique of choice for many high rate wireless communication systems. An overview of OFDM for a DSP/wireless beginner was given in this article where visualizations of how OFDM slices the spectrum into multiple subcarriers for one user was provided in detail. Orthogonal Frequency Division Multiple Access (OFDMA) is an extension of OFDM for multiple users, i.e., it is a multiple access technology (like TDMA and CDMA from 2G and 3G cellular systems, respectively) in which the available spectrum is divided into multiple subcarriers that are shared among multiple users. This was the choice

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