Spectrum of the Nyquist pulse and its symbol rate shifted version exhibit a spectral null at 0.5 symbol rate for a 0.5 timing offset
Wireless/SDR

What is a Symbol Timing Offset and How It Distorts the Rx Signal

Timing synchronization is one of the most fascinating topics in the field of digital communications. On the bright side, numerous scientists have contributed towards its body of knowledge due to its crucial role in the successful implementation of communication and storage systems. On the not-so-bright side, this knowledge has grown to an extent that it has also become the least understood and puzzling topic in the grand scheme of things. My objective in this article is to simplify the problem in a clear and intelligible manner, and also refer to some of the most widely used solutions within the explanation.

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Scatter plot for a QPSK signal after filtering through a channel
Wireless/SDR

An Introduction to Constant Modulus Algorithm (CMA)

In many kinds of equalizers such as maximum likelihood sequence estimation, the channel response is available at the Rx through any channel estimation procedure that requires a training sequence. For adaptive equalization such as Least Mean Square (LMS) equalizers or Decision Feedback Equalization (DFE), first the training sequence symbols and then symbol decisions are employed to tune the equalizer taps. There are many applications, however, where the Rx needs to acquire the equalizer coefficients without any help from the Tx in the form of known symbols. This is a non-data-aided scenario that is primarily required in mobile communication systems where

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A block diagram for the implementation of the feedforward phase estimator
Wireless/SDR

How to Estimate the Carrier Phase

In this article, I will describe how to estimate the carrier phase from an incoming waveform in a feedforward manner. This algorithm utilizes a sequence of known pilot symbols embedded within the signal along with the unknown data symbols. Such a signal is sent over a link in the form of separate packets in burst mode wireless communications. In most such applications with short packets, the phase offset $\theta_\Delta$ remains constant throughout the duration of the packet and a single shot estimator is enough for its compensation. Here, the primary task of the designer is to develop this closed-form expression

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Conventional network coding
Wireless/SDR

Physical Layer Network Coding (PNC)

A wired channel such as an optical fiber or a coaxial cable carries the communication signal within a confined material. In contrast, a wireless channel has a broadcast nature in which the transmitted signal propagates in a 3D space in several directions. This gives rise to the multipath nature of this medium. In a multiuser scenario, this problem takes an interesting turn. A signal transmitted by any node reaches several nodes due to this property. Except the one for which the signal is intended, each node treats this transmission as an interference which is overcome through careful receiver design or

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Linear approximation of atan2
DSP

3 Ways to Approximate atan2( ) in Hardware

When we think about signal processing, the focus is usually magnitude response of a system. However, in several DSP applications, the signal phase holds as much, if not more, significance as the magnitude response. For example, in digital FM demodulation, carrier phase synchronization and RF ranging, the phase (found through arctangent in four quadrants) of a complex signal needs to be computed by an FPGA or a DSP for further processing. In image processing applications, such an operation is also required to calculate the gradient orientations used in several popular feature descriptors like the Scale-Independent Feature Transform (SIFT) or the

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