5. Phase Modulation (PM) // Analog Communications // bhaswanth

PM is the dual of FM, related by an integration. We have written the equations already; let us spend a moment on where it appears separately.

In the analog era, "PM" mostly meant FM in disguise (with an integrator at the input or output to convert one to the other). Pure PM systems were rare in commercial broadcasting because broadcast audio is integrated easily anyway, and FM hardware was simpler.

Phase modulation takes center stage in digital communications, where binary or M-ary phase shifts encode bits. Binary phase-shift keying (BPSK) is PM with $m(t)$ taking only two values (say, 0 and $\pi$ radians). Quadrature phase-shift keying (QPSK) uses four phases (0, $\pi/2$ , $\pi$ , $3\pi/2$ ). Higher-order PSK uses 8, 16, 32 phases. We will return to all of this in Chapter 12.

In analog hardware, "PM" most commonly appears in two niches:

Indirect FM generation. The Armstrong method described above starts with PM (an integrator on $m$ , then a small phase modulator) at low carrier frequency and multiplies up.
PM in radar and ranging. Some pulse compression radars phase-code their pulses (Barker codes, pseudo-random sequences) to gain processing gain; this is PM modulating individual radar pulses. Same for GPS, where the L1 carrier is BPSK modulated by the C/A code.

The key takeaway is that PM and FM are mathematically isomorphic: a derivative or an integrator on the message converts one to the other, and most of what we said about FM (Bessel spectra, Carson bandwidth, capture effect, limiter advantage) applies to PM with appropriate modifications.