Synchronization circuit for a Minimum Shift Keying (MSK) modem

Carrier and Clock Synchronization in MSK Signals

Minimum Shift Keying (MSK) is a versatile and spectrally efficient digital modulation scheme. On this website, I have previously written a tutorial on MSK in some detail. We saw how MSK is a special case of Continuous-Phase Frequency Shift Keying (CPFSK) which is a special case of Continuous-Phase Modulation (CPM). We also explored how it can also be cast as Offset Quadrature Phase Shift Keying (OQPSK). In designing a real communication system, the design of modulators and demodulators is the easy part. The main difficulty arises from acquiring synchronization with the incoming signal. Today we investigate the carrier and timing

Continue reading
Individual and cascade frequency responses as well as group delays of the IIR and all-pass filters combination

FIR vs IIR Filters – A Practical Comparison

When it comes to practical applications, digital filter design is one of the most important topics in digital signal processing. Today we discuss a critical question encountered in filter design: how to compare the Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters. Since there is no clear winner, answering this question enables a designer to choose the right solution for their product. A brief comparison of FIR vs IIR filters is now explained below. Computational Complexity It is well known that most practical signals are simply sums of sinusoids. This implies that signals with sharp transition in time

Continue reading
Multiple paths arriving at the Rx with different strengths and delays

Carrier Phase-Based Ranging in Indoor Multipath Channels

Indoor positioning is one of the core technologies behind the idea of Internet of Things (IoT). Some of the use cases are asset tracking and management, factory automation systems, virtual and augmented reality applications, social media relevance and precision marketing in shopping malls. Distances between wireless devices can be determined through various ranging techniques that were introduced in the big picture of localization. Among the candidates, phase based ranging is a low-cost and accurate method that can be implemented on cheap hardware and deployed in real scenarios with relative ease (even in the absence of synchronization among nodes). In this

Continue reading
A composite channel model consisting of a pulse shaping filter, baseband channel and a matched filter

Channel Estimation in Wireless Communication

Channel estimation is a special case of the system identification problem that has a long history in the field of signal processing. The most common method to estimate a channel at the Rx is based on a training sequence (i.e., a data-aided scenario). The strategies below explain the fundamental idea of channel estimation in single-carrier systems that are still used by most advanced channel estimation techniques (aided by fancy mathematical modifications in subsequent steps). Channel estimation in OFDM systems is a topic of another article. System Parameters In this article, the modulation symbols are denoted by $a[m]$ while the channel

Continue reading
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

Why the Performance of an Equalizer Depends on Symbol Timing Phase

This post is written on an advanced topic mainly for practitioners and researchers in the design of wireless systems. For learning about wireless communication systems from a DSP perspective (the idea behind SDRs), I recommend you have a look at my book. One of the main questions in the design of a wireless receiver is the interactions among the three main blocks, namely the timing recovery loop, the equalizer and the carrier recovery loop. Life would have been easy if input to any of these blocks was independent of the output from the others. That obviously is not the case.

Continue reading