# 7.1 Digital receiver: carrier recovery

 Page 1 / 3
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?)

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
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 ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
Got questions? Join the online conversation and get instant answers! By Mldelatte   By Rhodes      