# 7.1 Digital receiver: carrier recovery

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The phase-locked loop (PLL) is a critical component in coherent communications receivers that is responsible for locking on to the carrier of a received modulated signal. A PLL adjusts the phase of a numerically-controlled oscillator to match that of the received signal. You will simulate a carrier recovery sub-system in MATLAB and then implement the sub-system on the DSP.

## Introduction

After gaining a theoretical understanding of the carrier recovery sub-system of a digital receiver, you will simulate the sub-system in MATLAB and implement it on the DSP. Thesub-system described is specifically tailored to a non-modulated carrier. A complete implementation will requiremodifications to the design presented.

The phase-locked loop ( PLL ) is a critical component in coherent communications receivers thatis responsible for locking on to the carrier of a received modulated signal. Ideally, the transmitted carrier frequencyis known exactly and we need only to know its phase to demodulate correctly. However, due to imperfections at thetransmitter, the actual carrier frequency may be slightly different from the expected frequency. For example, in theQPSK transmitter of Digital Transmitter: Introduction to Quadrature Phase-ShiftKeying , if the digital carrier frequency is $\frac{\pi }{2}$ and the D/A is operating at 44.1 kHz, then the expected analog carrier frequency is ${f}_{c}=\frac{\frac{\pi }{2}}{2\pi }\times 44.1=11.25\mathrm{kHz}$ . If there is a slight change to the D/A sample rate (say ${f}_{c}=44.05\mathrm{kHz}$ ), then there will be a corresponding change in the actual analog carrier frequency( ${f}_{c}=11.0125\mathrm{kHz}$ ).

This difference between the expected and actual carrier frequencies can be modeled as a time-varying phase. Providedthat the frequency mismatch is small relative to the carrier frequency, the feedback control of an appropriately calibratedPLL can track this time-varying phase, thereby locking on to both the correct frequency and the correct phase.

## Numerically controlled oscillator

In a complete coherent receiver implementation, carrier recovery is required since the receiver typically does notknow the exact phase and frequency of the transmitted carrier. In an analog system this recovery is oftenimplemented with a voltage-controlled oscillator ( VCO ) that allows for precise adjustment of the carrier frequency based on the output of aphase-detecting circuit.

In our digital application, this adjustment is performed with a numerically-controlled oscillator ( NCO ) (see [link] ). A simple scheme for implementing an NCO is based on the followingre-expression of the carrier sinusoid:

$\sin ({\omega }_{c}n+{\theta }_{c})=\sin \theta (n)$
where $\theta (n)={\omega }_{c}n+{\theta }_{c}$ ( ${\omega }_{c}()$ and ${\theta }_{c}()$ represent the carrier frequency and phase, respectively). Convince yourself that this time-varyingphase term can be expressed as $\theta (n)=\sum_{m=0}^{n} {\omega }_{c}+{\theta }_{c}$ and then recursively as
$\theta (n)=\theta (n-1)+{\omega }_{c}$
The NCO can keep track of the phase, $\theta (n)$ , and force a phase offset in the demodulating carrier by incorporating an extra term in this recursiveupdate:
$\theta (n)=\theta (n-1)+{\omega }_{c}+{d}_{\mathrm{pd}}(n)$
where ${d}_{\mathrm{pd}}(n)$ is the amount of desired phase offset at time $n$ . (What would ${d}_{\mathrm{pd}}(n)$ look like to generate a frequency offset?)

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There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
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da
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Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
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Application of nanotechnology in medicine
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I only see partial conversation and what's the question here!
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please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
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Professor
I think
Professor
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LITNING
scanning tunneling microscope
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Rafiq
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Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
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analytical skills graphene is prepared to kill any type viruses .
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
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what school?
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biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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