Passband Frequency Shift Keying (FSK)

Transmission of Binary Data by FSK

Whenever digital data needs to be transmitted over a communication channel, the information must first be converted into signals that the channel can carry. Two common transmission methods are: Baseband Transmission or Bandpass Transmission

Baseband transmission sends digital pulses directly through a low-pass communication channel. Bandpass transmission first modulates the data onto a high-frequency carrier before transmission.

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Frequency Shift Keying (FSK)

FSK represents binary information by changing the carrier frequency. The amplitude remains constant.

Binary Data

FSK Waveform

Binary 0 → Low frequency
Binary 1 → High frequency

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Why FSK and PSK are Preferred

Wireless transmitters and satellite communication systems often contain nonlinear amplifiers. Amplitude distortion can affect ASK because information is stored in the signal amplitude. FSK and PSK maintain a nearly constant envelope, making them much more resistant to nonlinear distortion.

Therefore,

• ASK is simple but more sensitive to noise and amplitude distortion.
• FSK is more reliable than ASK.
• PSK offers the best performance and is widely used in modern communication systems.

The band-pass binary FSK signal may be described directly as

$$ s(t)=A_c\cos(2\pi f_ct) \qquad \text{for symbol 1} \tag{9.3} $$

If we define the carrier frequency \(f_c\) as the midpoint between \(f_1\) and \(f_2\), that is,

$$ f_c=\frac{f_1+f_2}{2} $$

then we may represent the FSK signal as

$$ s_1(t)=A_c\cos\!\left[2\pi(f_c+\Delta f)t\right] \qquad \text{for symbol 1} \tag{9.4} $$

$$ s_0(t)=A_c\cos\!\left[2\pi(f_c-\Delta f)t\right] \qquad \text{for symbol 0} \tag{9.5} $$

By inspection of Eq. (9.4) and Eq. (9.5), we identify the complex baseband equivalent signals as

$$ \tilde{s}_1(t)=A_ce^{j2\pi\Delta ft} \qquad \text{for symbol 1} $$

$$ \tilde{s}_0(t)=A_ce^{-j2\pi\Delta ft} \qquad \text{for symbol 0} \tag{9.6} $$

While these complex baseband equivalents have a compact description, they differ from the baseband line codes discussed previously. In the following sections we evaluate the performance of ASK, FSK, and PSK receivers in the presence of additive white Gaussian noise.

The discussion concentrates on coherent detection because it provides an excellent reference for comparing the performance of different digital modulation techniques.

Frequency Shift Keying (FSK) is a digital modulation technique where digital information is transmitted by varying the frequency of a high-frequency carrier wave. Unlike ASK (which varies amplitude) or PSK (which varies phase), FSK encodes bits by switching between discrete carrier frequencies.

The simplest form is Binary FSK (BFSK), which uses two frequencies: the "mark" frequency \( f_1 \) for binary '1' and the "space" frequency \( f_2 \) for binary '0'. Each frequency is transmitted for a duration of one bit \( T_b \). Passband FSK signals occupy frequency bands around these carriers, making them suitable for transmission over RF links, optical channels, or other band-limited media.

Baseband Signal: The input digital data represented as voltage levels (e.g., +V for binary '1', -V for binary '0'). This signal has frequency components centered around zero.

Passband Signal: The carrier is modulated in frequency according to the baseband signal: \[ s(t) = \begin{cases} A_c \cos(2 \pi f_1 t + \phi), & \text{for binary '1'} \\ A_c \cos(2 \pi f_2 t + \phi), & \text{for binary '0'} \end{cases} \] Here, \(A_c\) is the carrier amplitude, \(f_1\) and \(f_2\) are the mark and space frequencies, and \(\phi\) is the initial phase.

A Passband FSK transmitter usually employs a Voltage-Controlled Oscillator (VCO) or a frequency synthesizer. The digital input stream modulates the carrier frequency via the VCO. The carrier amplitude remains constant, while the frequency changes according to the input bit.

VCO Principle:

A Voltage-Controlled Oscillator (VCO) generates a frequency proportional to the input control voltage. For FSK, the input binary signal is converted to voltage levels that control the VCO frequency.

For an LC tank VCO with a varactor diode (capacitance \( C' \) depends on reverse-bias voltage), the frequency is:
\[ f = \frac{1}{2 \pi \sqrt{L(C + C')}} \] Higher control voltage (binary '1') reduces \( C' \), increasing frequency to \( f_1 \). Lower voltage (binary '0') increases \( C' \), decreasing frequency to \( f_2 \).

Passband FSK Receiver (Coherent Demodulation):

Coherent BFSK receivers require local oscillators synchronized with the transmitted mark and space frequencies. The received passband signal is split into two branches: one for detecting \( f_1 \) (mark) and one for detecting \( f_2 \) (space).

In each branch, the received signal is multiplied by a locally generated carrier of the corresponding frequency and phase. The product is passed through a low-pass filter (LPF), which removes the high-frequency components and leaves a DC or low-frequency signal proportional to the transmitted bit energy. These outputs are compared in a decision device:

• If the \( f_1 \) branch output > \( f_2 \) branch output, the bit is detected as '1'.
• If the \( f_2 \) branch output > \( f_1 \) branch output, the bit is detected as '0'.

Mathematical Representation:

When a binary '1' is transmitted:

\( s(t) = A \cos(2\pi f_1 t) \)
Multiplier outputs:
\(\text{Branch } f_1: A \cos(2\pi f_1 t) \cdot A \cos(2\pi f_1 t) = \frac{A^2}{2}[1 + \cos(4\pi f_1 t)]\)
LPF output: \( \frac{A^2}{2} \)
\(\text{Branch } f_2: A \cos(2\pi f_1 t) \cdot A \cos(2\pi f_2 t) = \frac{A^2}{2}[\cos 2\pi(f_1+f_2)t + \cos 2\pi(f_1-f_2)t] \)
LPF output: 0

Decision: Output is binary '1' because LPF of \( f_1 \) branch > LPF of \( f_2 \) branch.

When a binary '0' is transmitted:

\( s(t) = A \cos(2\pi f_2 t) \)
Multiplier outputs:
\(\text{Branch } f_1: A \cos(2\pi f_2 t) \cdot A \cos(2\pi f_1 t) = \frac{A^2}{2}[\cos 2\pi(f_1+f_2)t + \cos 2\pi(f_1-f_2)t]\)
LPF output: 0
\(\text{Branch } f_2: A \cos(2\pi f_2 t) \cdot A \cos(2\pi f_2 t) = \frac{A^2}{2}[1 + \cos(4\pi f_2 t)]\)
LPF output: \( \frac{A^2}{2} \)

Decision: Output is binary '0' because LPF of \( f_2 \) branch > LPF of \( f_1 \) branch.

Summary

In summary, Passband FSK is a robust modulation scheme suitable for noisy or band-limited channels. Its constant amplitude nature makes it resilient against amplitude distortions, though its spectral efficiency is lower than PSK.

Feature	ASK	FSK	PSK
Amplitude	Changes	Constant	Constant
Frequency	Constant	Changes	Constant
Phase	Constant	Constant	Changes
Noise Immunity	Low	Medium	High
Typical Applications	RFID, Optical Links	Bluetooth, Paging Systems	Wi-Fi, GPS, Satellite, Cellular Networks

✔ FSK changes frequency.

✔ PSK changes phase.

✔ FSK and PSK are generally preferred because they are more robust against noise and nonlinear channel effects.

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