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November 30, 2023 DSP / Localization

FMCW Radar Part 3 – Design Guidelines

The Bloom’s Taxonomy describes the levels of mastery one attains in a field. Its last two stages are Synthesis and Evaluation. This is where the masters can be differentiated from the experts. In a job interview, for example, a good technique to judge a candidate’s ability is to ask them where the system in question breaks. A little learning is a dangerous thing Drink deep, or taste not the Pierian spring There shallow draughts intoxicate the brain And drinking largely sobers us again While the first two parts of the FMCW radar series addressed the lower levels, Part 3 is

Three different cases for carrier frequency offset

May 17, 2017 Wireless/SDR

What is Carrier Frequency Offset (CFO) and How It Distorts the Rx Symbols

In Physics, frequency in units of Hz is defined as the number of cycles per unit time. Angular frequency is the rate of change of phase of a sinusoidal waveform with units of radians/second. \begin{equation*} 2\pi f = \frac{\Delta \theta}{\Delta t} \end{equation*} where $\Delta\theta$ and $\Delta t$ are the changes in phase and time, respectively. A Carrier Frequency Offset (CFO) usually arises due to two reasons. The video below also explains this concept. [Frequency mismatch between the Tx and Rx oscillators] No two devices are the same and there is always some difference between the manufacturer’s nominal specification and the

May 9, 2017 DSP

Moving Average Filter

The most commonly used filter in DSP applications is a moving average filter. In today’s world with extremely fast clock speeds of the microprocessors, it seems strange that an application would require simple operations. But that is exactly the case with most applications in embedded systems that run on limited battery power and consequently host small microcontrollers. For noise reduction, it can be implemented with a few adders and delay elements. For lowpass filtering, the excellent frequency domain response and substantial suppression of stopband sidelobes are less important than having a basic filtering functionality, which is where a moving average

OFDM slices the spectrum just like a bread

May 1, 2017 Wireless/SDR

A Beginner’s Guide to OFDM

In the recent past, high data rate wireless communications is often considered synonymous to an Orthogonal Frequency Division Multiplexing (OFDM) system. OFDM is a special case of multi-carrier communication as opposed to a conventional single-carrier system. The concepts on which OFDM is based are so simple that almost everyone in the wireless community is a technical expert in this subject. However, I have always felt an absence of a really simple guide on how OFDM works which can prove useful for technical persons not wanting to deal with too much technicalities, such as DSP experts outside communications, computer programmers, ham

Multipath components with large Doppler shifts compared to the signal bandwidth

January 20, 2022 Wireless/SDR

Slow and Fast Fading in Wireless Channels

We discussed the idea of fading in wireless channels in a previous article. To understand different types of fading in the context of time variations, refer to the figure below that shows a multipath channel. Slow Fading A slow motion scenario is illustrated in the figure below where three multipath components are arriving with Doppler shifts $F_{D,i}$ from the carrier frequency. In this scenario, the magnitudes of $F_{D,i}$ are small and hence observe very little spreading of the cumulative spectrum. This can be understood by recalling that when two sinusoids with two different frequencies $F_1$ and $F_2$ are added, the