# Carrier Acquisition, Need for Carrier Acquisition & Techniques

**What is Carrier Acquisition? The Need For Carrier Acquisition & Its Techniques**

**What is Carrier Acquisition?**

In suppressed carrier communication, the demodulation process requires an identical local carrier at the demodulator. This local carrier needs to have same frequency and phase as the transmitted signal. which is acquired using **carrier acquisition.**

The process of acquiring or extracting carrier frequency from the received signal is called

carrier acquisition.

**Why We Need Carrier Acquisition?**

**Amplitude Modulated Suppressed Carrier** signal needs a locally generated signal having the same phase and frequency as the received signal (**carrier signal**).

If the frequency or phase of the signal is different than the received signal, then the demodulated message signal we get will be **distorted** or may be completely **destroyed**. To avoid such problems and get a clear message signal, we need an **identical carrier**.

**Suppose** we receive a **DSB-SC** signal which is **m(t)cos(ω _{c}t + ϴ_{i})** and the carrier generated by demodulator has a frequency

**(ω**and phase

_{c}+Δω)**ϴ**i.e. the local carrier is

_{o}**2cos((ω**.

_{c}+Δω)t+ϴ_{o})Thus the demodulated signal **e(t)** will be:

**e(t) = m(t) cos(ω _{c}t + ϴ_{i}) 2cos((ω_{c}+Δω)t+ ϴ_{o})**

**e(t) = 2m(t) cos(ω _{c}t + ϴ_{i}) cos((ω_{c}+Δω)t+ ϴ_{o})**

**e(t) = m(t) [cos {(ω _{c}+ω_{c}+Δω) t +ϴ_{i}+ϴ_{o}} + cos(Δωt+ ϴ_{i}-ϴ_{o})]**

**e(t) = m(t) cos {(ω _{c}+ω_{c}+Δω) t +ϴ_{i}+ϴ_{o}} + m(t)cos(Δωt+ ϴ_{i}-ϴ_{o})**

By passing through **Low-pass filter**

**e(t) = m(t)cos(Δωt+ ϴ _{i}-ϴ_{o})**

If the frequency difference **Δω = 0** and phase difference **(ϴ _{i}-ϴ_{o}) = 0**. Then

**e(t) = m(t)**

Which means the message signal is **successfully** received.

However, if the frequency difference **Δω = 0** and phase difference **(ϴ _{i}-ϴ_{o}) ≠0**. Then

**e(t) = m(t)cos(ϴ _{i}-ϴ_{o})**

This means that the message signal is **attenuated** by factor **cos(ϴ _{i}-ϴ_{o})**. if

**(ϴ**, then

_{i}-ϴ_{o})= π/2**e(t) = 0**and the message signal is

**completely destroyed**.

Another case is if the phase difference **(ϴ _{i}-ϴ_{o}) =0** and frequency difference

**Δω ≠ 0**. Then

**e(t) = m(t)cos(Δωt)**

This equation implies that the same message signal is multiplied with a sinusoid of frequency **Δω**. **Δω** is usually very **small**. which means that the message signal will go from maximum to zero at the rate of two times its frequency. This is called **beating effect**. This beating effect **distorts** the original signal even if the Δω is very small.

- Related Post: Quantization & Sampling? Types & Laws of Compression

**Techniques Of Carrier Acquisition**

There are few different techniques used for carrier acquisition. Some of them are given below.

**Phase-Locked Loop (PLL)**

**Phase locked loop**, commonly known as **PLL** is one of the most widely used circuit for **carrier acquisition**. It tracks the phase and frequency of the incoming/reference signal and generates a stable frequency signal.

A **PLL** is made up of 3 components

- VCO
- Phase detector
- Loop filter

**VCO**

**VCO** stands for the voltage controlled oscillator. It generates frequency signal, which is controlled by an external voltage signal. The frequency signal produced by VCO is

**ω(t) = ω _{c }+ ce_{o}(t)**

**ω _{c }**is

**free running frequency**when external voltage e

**is zero.**

_{o}(t)**C**is

**constant**of VCO &

**e**

**is the external voltage signal. The frequency is increased or decreased according to this voltage signal**

_{o}(t)**e**

**.**

_{o}(t)**Phase Detector**

A Multiplier is used as a **phase detector**. It has 2 input signals, a reference signal & the output of VCO.

It generates a signal proportional to the **phase difference **between the two signals.

Suppose the input signal is **Asin(ω _{c}t + ϴ_{i})** & output is

**Bcos(ω**,then its product is

_{c}t + ϴ_{o})**e(t) = Asin(ω _{c}t + ϴ_{i}) **

**B**

**cos(ω**

_{c}t + ϴ_{o})**e(t) = AB/2 sin(2ω _{c}t + ϴ_{i }+ ϴ_{o}) + AB/2 sin(ϴ_{i }– ϴ_{o})**

The high-frequency term is filtered the **loop filter** discussed below.

**Loop Filter**

This **loop filter** is actually a **narrow band low pass filter**. It blocks any high-frequency components from its input signal (**output of multiplier**) and generates a **dc voltage**. which is supplied as input to the **VCO.**

The signal after passing through **loop filter** becomes

**e _{o}(t) = AB/2 sin(ϴ_{i }– ϴ_{o})**

If the phase difference **(ϴ _{i }– ϴ_{o})** is not

**zero**then the signal

**e**will generate

_{o}(t)**DC**voltage & supplies to the

**VCO.**This voltage leads to increment in the

**VCO**frequency.

The process is repeated until the frequency & phase matches the input signal. Such case is called **in phase lock **or **phase coherent **state.

**Carrier Acquisition In DSB-SC**

In **DSB-SC** scheme the level carrier can be regenerated using two methods discussed below.

**Signal Squaring Method:**

This method is used for carrier acquisition in **DSB-SC** communication.

The block diagram of **signal-squarer** is given below.

The received DSB-SC signal **x(t)** is first passed through a **squarer**, which takes the square of the signal.

The received signal **x(t)** is:

**x(t) = m(t)cos ω _{c}t**

The output **y(t)** of squarer is:

**y(t) = x ^{2}(t)**

**y(t) = (m(t)cos ω _{c}t)^{2}**

**y(t) = m ^{2}(t)cos^{2} ω_{c}t**

**y(t) = ½ m ^{2}(t)(1+cos 2ω_{c}t)**

**y(t) = ½ m ^{2}(t)+ ½ m^{2}(t)cos 2ω_{c}t**

As we can see, **m ^{2}(t)** is a non-negative signal i.e. it is positive for every value of

**t**. Therefore, it has positive average (DC) value.

Let suppose the average value of **m ^{2}(t)/2** is

**k**then

**½ m ^{2}(t) = k + ϕ(t)**

Now the signal **y(t)** can be expressed as:

**y(t) = ½ m ^{2}(t)+ (k + ϕ(t))cos 2ω_{c}t**

**y(t) = ½ m ^{2}(t)+ k cos 2ω_{c}t + ϕ(t)cos 2ω_{c}t**

After passing through the narrow-band band-pass filter, it will block **m ^{2}(t) **completely because of its

**ω=0**.

**k cos 2ω**will flow through. However, some parts of

_{c}t**ϕ(t)cos 2ω**will also flow out because it has almost no power at

_{c}t**2ω**. Thus the signal

_{c}**y**becomes:

_{0}(t)**y _{0}(t) = k cos 2ω_{c}t + ϕ(t)cos 2ω_{c}t**

The next stage is **PLL**. The **PLL** will block any **residual frequencies** & produce a **stable frequency** signal** z(t)**, which is :

**z(t) = k cos 2ω _{c}t**

The last stage of **signal squarer** is the **divider**. The divider divides the frequency of the input signal by two. Thus the output signal becomes a pure sinusoidal wave of frequency **ω _{c}**.

The output **r(t)** of signal squarer is:

**r(t) = k cos ω _{c}t**

**COSTAS Loop**

**John P.Costas** was an Electrical engineer. In 1950, he invented the method to use a **modified PLL** to regenerate the carrier signal in suppressed carrier communication. This circuit is known as **Costas loop**.

Costas loop is used to acquire the carrier signal in DSB-SC communication.

**Block Diagram**

The **block diagram** of Costas loop is given below:

This diagram shows the received signal DSB-SC signal **m(t)cos(ω _{c}t+ϴ_{i})** is multiplied with local carriers

**cos(ω**&

_{c}t+ϴ_{o})**sin(ω**separately to get

_{c}t+ϴ_{o})**x**and

_{1}(t)**x**respectively.

_{2}(t)The VCO generates the local carrier **cos(ω _{c}t+ϴ_{o})**, which is phase shifted by

**–π/2**to generate

**sin(ω**.

_{c}t+ϴ_{o})The signal **x _{1}(t)** and

**x**is given by:

_{2}(t)**x _{1}(t) = m(t)cos(ω_{c}t+ϴ_{i}) cos(ω_{c}t+ϴ_{o})**

**x _{1}(t) = ½ m(t){cos(ϴ_{i}– ϴ_{o}) +cos(2ω_{c}t+ ϴ_{i} +ϴ_{o})}**

**x _{1}(t) = ½ m(t)cos(ϴ_{i}– ϴ_{o}) +½ m(t)cos(2ω_{c}t+ ϴ_{i} +ϴ_{o})**

**x _{2}(t) = m(t)cos(ω_{c}t+ϴ_{i}) sin(ω_{c}t+ϴ_{o})**

**x _{2}(t) = ½ m(t){sin(ϴ_{i}– ϴ_{o}) +sin(2ω_{c}t+ ϴ_{i} +ϴ_{o})}**

**x _{2}(t) = ½ m(t)sin(ϴ_{i}– ϴ_{o}) +½ m(t)sin(2ω_{c}t+ ϴ_{i} +ϴ_{o})**

The signal **x _{1}(t)** &

**x**is then passed through

_{2}(t)**low pass filter**, it blocks high frequency components & allow low frequency components. Thus producing

**y**&

_{1}(t)**y**for the signal

_{2}(t)**x**&

_{1}(t)**x**respectively.

_{2}(t)**y _{1}(t) = ½ m(t)cos(ϴ_{i}– ϴ_{o})**

**y _{2}(t) = ½ m(t)sin(ϴ_{i}– ϴ_{o})**

These two signals **y _{1}(t) **&

**y**are then multiplied to produce

_{2}(t)**z(t)**as:

**z(t) = ½ m(t)cos(ϴ _{i}– ϴ_{o}) ½ m(t)sin(ϴ_{i}– ϴ_{o})**

**z(t) = ⅛ m ^{2}(t){sin(0) + sin2(ϴ_{i}– ϴ_{o})}**

**z(t) = ⅛ m ^{2}(t) sin2(ϴ_{i}– ϴ_{o})**

Thus the signal **z(t)** will produce a DC voltage depending on the phase difference **(ϴ _{i}– ϴ_{o})**.

If there is any phase difference then this signal will produce DC voltage.

The **narrowband**** low-pass filter** will suppress any frequency components and produce a **pure DC signal**. This DC signal will either increase or decrease the frequency of the VCO.

When the frequency and phase of the input signal and matches the VCO output, then the phase difference **(ϴ _{i}– ϴ_{o}) = 0** and the

**DC**output of Narrowband LPF becomes

**0**. In such case, the VCO output remains

**unchanged**.

The output of the **VCO** is the acquired carrier we need & the signal **y _{1}(t)** is the demodulated message signal.

**y _{1}(t) = ½ m(t)cos(ϴ_{i}– ϴ_{o})**

**y _{1}(t) = ½ m(t)cos(0)**

**y _{1}(t) = ½ m(t)**

**Carrier Acquisition In SSB**

In **single sideband** (**SSB) communication**, the methods of **carrier acquisition** do not work as it did in the DSB-SC. The **signal-squaring** method & **Costas loop** does not work. The reason is that after **squaring** SSB signal, the product terms does not contain a pure sinusoid of the carrier frequency as in **DSB-SC**. So extracting the carrier through such method does not work.

However, if we transmit a carrier signal of low power with **SSB signal**, it can be extracted using a **narrowband band-pass filter**. The said signal is then amplified, in such way the demodulator will know the **frequency **&** phase** of the carrier signal.

**Vestigial Sideband (VSB)** has the same situation as **SSB** and it also needs a separate carrier with the transmitted signal.