Time domain formation of a Raised Cosine pulse for unity excess bandwidth

How Excess Bandwidth Governs Timing Recovery in Digital Communication Systems

In the article on pulse shaping, we described the excess bandwidth, also known as roll-off factor, as the extra fractional bandwidth required to shape the spectrum. As it turns out, this excess bandwidth is also crucial for accomplishing timing synchronization in single-carrier systems due to its participation in generating spectral timing lines. Spectral Timing Lines Since a data stream consists of a sequence of 1s and 0s, the signal waveform is not a pure clock. Instead, a series of 1s and 0s appear in random order. The purpose of timing synchronization is to extract a clock out of this waveform.

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QAM constellation diagrams for M = 4, 16 and 64

QAM Constellations in Digital Communication Standards

Quadrature Amplitude Modulation (QAM) is one of the most spectrally efficient modulation schemes. This is why it is used in a wide range of digital and wireless communication systems. Recently, Ref. [1] describes a list of QAM schemes used in the standards as below which I think can be useful for an interested reader. Standard QAM Alphabet Size $M$ Bits/Symbol $\log_2 M$ Digital Video Broadcasting – Cable (DVB-C) 16 to 256 4 to 8 Digital Video Broadcasting – Cable 2 (DVB-C2) 16 to 4096 4 to 12 Digital Video Broadcasting – Terrestrial (DVB-T) 16 and 64 4 and 6 Digital

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OFDM subcarriers in frequency domain

CDMA or OFDM

Reading about interference cancellation techniques today, I recalled an interesting article by Sridhar Vembu titled Two Philosophies in CDMA: A Stroll Down Memory Lane. Vembu is the founder and CEO of Zoho Corporation, a venture which has turned him into a billionaire. He spent time both in academia (at Princeton) and in industry (at Qualcomm) working with the likes of Sergio Verdu in one camp and Andrew Viterbi in the other. Here are some excerpts from his article which is not available online anymore at the time of this writing. I have now worked a little over 10 years in

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A machine press

Why the Constant e Arises in Complex Plane as a Rotation

In the tutorial on how complex numbers arose, we asked three questions. The first two were answered in the same article while the answer to the third question, repeated below, is explained here. Why is the expression $e^{i \theta}$ a rotation of 1 by $\theta$ radians on a unit circle? Is it possible to make sense out of a number like $2.71828^{\sqrt{-1}\cdot\theta}$? The constant e is a special number discovered by Jacob Bernoulli while studying compound interests. It appears in many other forms as well which are all related to each other but that topic is a complete account in

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(Top) An 8-PSK waveform. (Bottom) Two constellation diagrams: one at the Tx shown by thick red lines and the other at the Rx for a phase offset of 17 degrees shown by dotted purple lines

I/Q Signals 101: Neither Complex Nor Complicated

Dec 04, 2020 There was a recent discussion on GNU Radio mailing list in regards to the simplest possible intuition behind I/Q signals. Why is I/Q sampling required? Question: The original question from Kristoff went like this: “… when you mention `GNU Radio complex numbers’, you also have to mention I/Q signals, which is a topic that is very difficult to explain in 10 seconds to an audience who has never seen anything about I/Q sampling before.” Comment: According to Jeff Long: “This is a great thing to try to figure out. If we can come up with an answer

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