A channel with 8 taps demonstrating the main cursor, precursor ISI and postcursor ISI
Wireless/SDR

How Decision Feedback Equalizers (DFE) Work

We started the classification of equalization algorithms by introducing the need for equalization in wireless communication systems. We said that the wireless channel is a source of severe distortion in the received (Rx) signal and our main task is to remove the resulting Inter-Symbol Interference (ISI) from the Rx samples. Equalization refers to any signal processing technique in general and filtering in particular that is designed to eliminate or reduce this ISI before symbol detection. In essence, the output of an equalizer should be a Nyquist pulse for a single symbol case. A conceptual block diagram of the equalization process

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A prism decomposes the white light into 7 colours
DSP

The Discrete Fourier Transform (DFT)

Learned in some other articles on this website, the following three important concepts take us to the core of the Discrete Fourier Transform (DFT) idea. Regardless of the signal shape, most signals of practical interest can be considered as a sum of complex sinusoids oscillating at different frequencies. A set of $N$ orthogonal complex sinusoids can be constructed within a span of $N$ time domain samples. Each `tick’ or bin on the discrete frequency axis denotes the discrete frequency $k/N$ of such a complex sinusoid. To understand how a set of sinusoids with $N$ discrete frequencies can sum up to

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Block diagram of a 4 symbol communication system
Wireless/SDR

Packing More Bits in One Symbol

Note that digital electronics are constrained to work on only two levels by electronic switches which in the simplest case are either on or off. For many reasons, practical digital communication systems require quite complicated signal processing workload both at the Tx and Rx ends that can be performed only by a device more intelligent than an electronic switch, such as an Application Specific Integrated Circuit (ASIC), Field Programmable Gate Array (FPGA), Digital Signal Processor (DSP) or a General Purpose Processor (GPP). If this intelligent device can differentiate between two signal levels like a switch, it can certainly differentiate between

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Frequency domain beamforming implements a procedure for broadband signals that resembles the conventional narrowband beamformers
Wireless/SDR

Beamforming for Broadband Signals

Recall that classical or physical beamforming is based on calculating the differences in wave arrival times of a signal between antenna array elements and compensating for these delays through signal processing techniques that steer the beams in any desired direction. There are two main candidates for this purpose: Phase shifting and True Time Delays (TTD). We saw in that article on beamforming that phase shifts implemented through a set of complex multipliers are incapable of beamforming over the entire bandwidth of a signal. Why? The intuitive reason is clear from a signal level view. In the narrowband scenario, the same

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S-curve for decision-directed maximum likelihood phase error detector
Wireless/SDR

What are Cycle Slips and Hangup in Phase Locked Loops?

In a previous article, we have covered in detail the inner workings of a Phase Locked Loop (PLL) in a Software Defined Radio (SDR). There are two phenomena that have the potential to occasionally disrupt the performance of a PLL operating in steady state: cycle slips and hangup. Both the carrier and timing locked loops suffer from these issues. The underlying mathematics is quite intricate and hence I give a simple overview of these concepts. A reader interested in further exploration is referred to [1]. Cycle Slips To understand the cycle slip, assume that the loop is in tracking mode,

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