Digital vs analog modulation; GMSK

Advantages of digital over analog modulation

• Better noise and fading immunity; signals can be regenerated.
• Supports error detection/correction coding, encryption and source coding.
• Easy multiplexing of voice, data and video (TDMA, CDMA, OFDM).
• Higher spectral and power efficiency, and cheaper VLSI/DSP implementation.

GMSK modulation

Gaussian MSK is MSK in which the bipolar NRZ data passes through a Gaussian low-pass filter before frequency modulation with index h = 0.5. The filter smooths the phase trajectory, which reduces side lobes and out-of-band power. The 3 dB bandwidth–bit period product BT controls the shape: GSM uses BT = 0.3, and BT = ∞ gives MSK.

h_G(t) = (√π/α) exp(−π² t² / α²),  α = 0.5887 / B

Transmitter

NRZ -> [Gaussian LPF] -> [Integrator] -> φ(t)
data   (BT = 0.3)                        |
                    +---------+----------+
                    v                    v
                  [cos φ]              [sin φ]
                    |                    |
           cos ωct->(x)          sin ωct->(x)
                    +------(+)-----------+
                            |
                          GMSK

• The Gaussian filter spreads each bit over about 3 bit periods (controlled ISI).
• The filtered signal is integrated to give the phase φ(t); I = cos φ, Q = sin φ modulate quadrature carriers. (A simpler form feeds the filtered data directly to a VCO with h = 0.5.)

Receiver

GMSK->[BPF]-+->(x)->[LPF]->[Sample]->I-+
            |  cos                     |
            |                    [MLSE / ]->data
            +->(x)->[LPF]->[Sample]->Q-+ [decision]
               sin    ^
                 [Carrier & clock recovery]

• Coherent I/Q demodulation recovers the phase; I and Q are sampled at alternate bit instants as in MSK.
• Because the Gaussian filter adds ISI, GSM receivers use a Viterbi (MLSE) equalizer. Non-coherent detection with a limiter–discriminator is also possible.

Constellation (phase states)

            Q
            •
            |
     •------+------•  I
            |
            •
 Constant envelope; phase moves
 smoothly by ±π/2 per bit.

Merits: constant envelope (class-C amplifiers, long battery life), narrow spectrum (low adjacent channel interference), used in GSM, DECT and Bluetooth (GFSK variant).