MSK, GMSK and OFDM modulator/demodulator

MSK and GMSK

• MSK is continuous phase FSK with modulation index h = 0.5 (tone spacing R_b/2). Phase changes smoothly by ±π/2 per bit; constant envelope; can be seen as OQPSK with half-sine pulse shaping.
• GMSK is MSK whose data first passes a Gaussian low-pass filter (BT = 0.3 in GSM). This makes the spectrum very compact while keeping the constant envelope.

OFDM modulator

bits->[Map QAM]->[S/P]->[IFFT]->[P/S]->[Add CP]
                         N-pt               |
                                            v
                             RF <-[Up-conv]<-[DAC]

• Bits are mapped to QAM/PSK symbols and split into N parallel streams.
• The IFFT places each symbol on a separate orthogonal subcarrier (spacing 1/T_s) and produces one time-domain OFDM symbol.
• After P/S conversion a cyclic prefix longer than the channel delay spread is added, then DAC and RF up-conversion.

OFDM demodulator

RF->[Down-conv]->[ADC]->[Remove CP]->[S/P]->[FFT]
                                              |
                                              v
bits<-[Demap]<-[P/S]<-[One-tap equalizer (pilots)]

• After down-conversion and sampling, the CP is removed (it carries the ISI).
• The FFT separates the subcarriers: Y_k = H_k X_k + N_k.
• Each subcarrier is equalized by dividing by its channel estimate H_k, then demapped to bits.

OFDM turns a frequency-selective channel into many flat sub-channels, so it handles high data rates in multipath (Wi-Fi, LTE, 5G).