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DPSK transmitter/receiver and PN sequence

Short answer

DPSK encodes data as phase changes between successive bits, so the receiver multiplies the signal by its one-bit-delayed version without a coherent carrier. A PN sequence is a deterministic periodic maximal-length shift-register code with noise-like autocorrelation; it spreads/despreads signals, synchronizes receivers, and separates CDMA users.

Explain the transmitter and receiver of DPSK modulation scheme. Briefly explain about pseudo-noise (PN) sequence. Why is it used?

DPSK transmitter and receiver

Differential PSK (DPSK) is a non-coherent form of BPSK. The data is carried by the change of phase between successive bits, so the receiver does not need a coherent carrier reference.

Transmitter

m_k --->[XNOR]------+-----> [BPSK ] --> DPSK
          ^         | d_k   [mod  ]
          |         |          ^
          +-[Delay T_b]<-+   cos ωct
            d_(k−1)
  • Differential encoding: d_k = NOT(m_k ⊕ d_{k−1}). A "1" keeps the previous phase; a "0" changes it by π.
  • The encoded sequence d_k then BPSK-modulates the carrier.

Example (reference bit d₀ = 1):

m_k–10010110
d_k110110001
Phase00π00πππ0

Receiver

r(t)->[BPF]-+->(x)->[∫ over T_b]->[Decision]-> m_k
            |   ^
            +->[Delay T_b]

The received signal is multiplied by itself delayed by one bit. If the two bits have the same phase, the integrator output is positive (bit 1); if opposite, it is negative (bit 0). DPSK is simpler than coherent BPSK, but needs only about 1 dB more E_b/N₀ for the same BER at typical error rates: P_b = ½ exp(−E_b/N₀).

Pseudo-noise (PN) sequence

A PN sequence is a deterministic, periodic binary sequence that looks random. It is usually generated by an m-stage linear feedback shift register; a maximal-length (m-) sequence has period N = 2ᵐ − 1. Properties of an m-sequence:

  • Balance: number of 1s exceeds number of 0s by one.
  • Run property: half the runs have length 1, a quarter length 2, and so on.
  • Autocorrelation: 1 at zero shift and −1/N at any other shift (noise-like).

Why it is used

  • To spread and despread signals in DSSS and to set hop patterns in FHSS.
  • Its sharp autocorrelation lets the receiver synchronize and reject delayed multipath and interference.
  • Different (low cross-correlation) codes give each user a separate channel in CDMA, and provide privacy.

✓ Answer checked by Claude Opus 5.5 (high effort)

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