Raised Cosine Archives

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

January 17, 2022 Wireless/SDR

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.

October 31, 2020 Wireless/SDR

Mueller and Muller Timing Synchronization Algorithm

Proposed in 1976, Mueller and Muller algorithm is a timing synchronization technique that operates at symbol rate, as opposed to most other synchronization algorithms that require at least 2 samples/symbol such as early-late and Gardner timing error detectors. All of these are feedback techniques that operate within a PLL. Feedforward methods such as digital filter and square timing synchronization are also feasible due to powerful digital signal processing that avoids feedback problems such as hangups. The most confusing thing communication engineers and radio hobbyists find about Mueller and Muller algorithm algorithm is the cross product in its expression: matched filter

At the boundary of two OFDM symbols, pulse shaping smoothes the edges, resulting in the avoidance of spectral regrowth

February 26, 2020 Wireless/SDR

Windowing an OFDM Signal in Time Domain

Orthogonal Frequency Division Multiplexing (OFDM) has been introduced in a previous article as a technique suitable for high data-rate transmissions over a wireless channel. The two main advantages I mentioned were as follows: Simple one-tap equalization, and Ability to slice the spectrum and utilize each slice in an independent manner. Due to these advantages, it was adopted as the preferred modulation in WiFi and 4G-LTE systems. The interesting part is that while many new waveforms were proposed to replace it in 5G NR, OFDM was still the modulation of choice for both downlink and uplink directions with some minor changes.

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

February 21, 2020 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.

Square-root Nyquist filters for three different excess bandwidths

September 16, 2017 DSP / Wireless/SDR

How to Design Nyquist and Square-Root Nyquist Pulse Shaping Filters

The radio spectrum is a very precious resource like real estate and must be utilized judiciously. Pulse shaping filters control the spectral leakage of the transmitted signal in a wireless channel due to the strict restrictions to comply with a spectral mask. This is even more important for the upcoming 5G wireless systems which are based on a variety of wireless transmission protocols (such as mobile networks, Internet of Things (IoT) and machine to machine communications) combined in one comprehensive standard. Even for wired channels, there is always a natural bandwidth of the medium (copper wire, coaxial cable, optical fiber)