Intuition behind LMS algorithm

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

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Experimental setup for low SNR receiver

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

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OFDM subcarriers in frequency domain

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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Beamforming in multi-user vs massive MIMO systems

Zero-Forcing (ZF) Detection in Massive MIMO Systems

Massive MIMO is one of the defining technologies in 5G cellular systems. In a previous article, we have described spatial matched filtering (or maximum ratio) as the simplest algorithm for signal detection. Here, we explain another linear technique, known as Zero-Forcing (ZF), for this purpose. It was described before in the context of simple MIMO systems here. Background Consider the block diagram for uplink of a massive MIMO system as drawn below with $N_B$ base station antennas and $K$ mobiler terminals. It is evident that the cumulative signal at each base station antenna $j$ is a summation of signals arriving

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A quasi-static assumption implies that the channel stays the same for each block but varies from one block to the next

A Time-Varying Wireless Channel

Today we will discuss three strategies that are usually adopted for handling a wireless channel that is varying with time and hence acting differently on different data symbols. For a channel impulse response $c(t)$, number of multipath $N_{MP}$, channel gains $\gamma_i(t)$ and delays $\tau_i(t)$ for the $i$-th path, respectively, we can write \begin{equation*} c_B(t) = \sum _{i=0}^{N_{MP} -1} \gamma_i(t) \cdot \delta(t-\tau_i(t)) \end{equation*} i.e., channel gains $\gamma_i(t)$ and channel delays $\tau_i(t)$ are varying with time albeit at different rates. With the movement in the channel, the taps in a frequency selective channel are changing according to the rotation rates of path

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