CM · Digital modulation

Digital Modulation: ASK, FSK, PSK

A sinusoidal carrier has only three knobs to turn: amplitude, frequency, and phase. Switching one of them between two values according to the bits gives ASK, FSK, or PSK, respectively. This unit loads the same bit string all three ways and asks which one holds up best against noise.

Same bits, three knobs

Press ASK, FSK, and PSK in turn, and the bit string 1 0 1 1 0 drawn as a staircase on top rides on the blue carrier below in three different shapes. In ASK the amplitude switches on and off, in FSK the crest spacing splits into two widths, and in PSK the waveform flips upside down at every boundary where the bit changes.

The knob being switched

ASK : A → {0, 1}

Amplitude · noise-prone

Three knobs of the carrier

A single sinusoid is written s(t) = A cos(2π f t + φ). The only quantities in it that can be changed are the amplitude A, the frequency f, and the phase φ. Digital modulation pairs bits 0 and 1 with two values of one of these quantities and clicks that knob over every time the bit changes. Which knob gets turned is what names the scheme.

ASK, FSK, PSK

ASK switches the amplitude on and off. Sending the carrier for a 1 and silencing it for a 0 is the simplest scheme of all, but because the information sits in the amplitude, noise on the amplitude shakes it directly. FSK keeps the amplitude constant and switches the frequency between two values, so amplitude noise bothers it less; in the plot the crests crowd together where the staircase is high and spread out where it is low. PSK holds both amplitude and frequency fixed and flips the phase between 0 and π. At the same signal power, 0 and π are the two points farthest apart in signal space, which makes PSK the most noise-robust of the three.

Observes(t) = A cos(2π f t + φ)

There are three knobs: amplitude A, frequency f, and phase φ.

ChooseΔφ → ?

Switching the phase is PSK.

Grouping bits into symbols

Raise the number of phases from two to four or eight, and each symbol carries more bits. With M phases a symbol carries n = log₂ M bits, so 4-PSK carries 2 bits per symbol and 8-PSK carries 3. The catch is that crowding more points onto the same circle narrows the gaps between them, which makes the scheme more vulnerable to noise. That trade between the urge to send faster and the margin to withstand noise leads into the next unit on bandwidth and symbol rate.

Fill inn = log₂ ?

With M phases, each symbol carries log₂ M bits.

On your ownRb = n · ?

bit rate = bits per symbol × symbol rate.

Back to the first screen

In ASK the carrier was on only where the bit was 1 and off where it was 0. In FSK the amplitude stayed the same while only the crest spacing split into two widths, and in PSK the waveform was flipped upside down in every stretch where the bit was 0. All three put the same bit string on the same carrier; the only difference was which knob they turned, amplitude, frequency, or phase. And at equal power, the one most robust to noise was PSK, the scheme that uses phase.

Digital modulation sends bits on one knob of a carrier. ASK switches the amplitude, FSK the frequency, and PSK the phase between two values according to the bits. In PSK the two phases 0 and π lie farthest apart, so at equal power it is the most robust to noise. M-ary schemes that raise the number of phases to M carry n = log₂ M bits per symbol, with a bit rate of Rb = n Rs.

In the next unit

Sending symbols faster or packing more bits into each one raises the speed, but both roads have limits. The next unit looks at how fast symbols can go within a given bandwidth and how symbol rate and bandwidth are tied together. The starting points are the Nyquist signaling rate and spectral efficiency, which counts how many bits travel per 1 second per 1 hertz.