---
title: "DPSK transmitter/receiver and PN sequence"
subject: "Wireless Communication"
chapter: 4
key: "semester_7/wireless_communication:dpsk-pn-sequence"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/dpsk-pn-sequence
site: BCT Engineering
---

# DPSK transmitter/receiver and PN sequence

Wireless Communication · Chapter 4: Modulation and Demodulation in Mobile Communication

- Asked in: 2072 Magh, 4+2+2 marks
- Video: [Lecture-24|Wireless Communications|Spread Specturm Modulation - PN sequence & DS-SS](https://www.youtube.com/watch?v=7XwWuD4IYOA) — Prof.Ashish Tiwari
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/dpsk-pn-sequence
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-4

## Question

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

## 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.

## Answer

#### 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**
```text
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 | – | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|---|
| d_k | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| Phase | 0 | 0 | π | 0 | 0 | π | π | π | 0 |

**Receiver**
```text
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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How does DPSK carry information?
   A. In the change of phase between successive bits, so no coherent carrier reference is needed
   B. In absolute carrier phase, needing coherent reference
   C. In the carrier frequency hop pattern
   D. In the amplitude of each bit
   Answer: A. DPSK differentially encodes data, so the receiver compares each bit with the previous one. (Key point: DPSK principle)

2. How does the DPSK receiver decide a bit?
   A. It multiplies with a PN code and compares to zero
   B. It multiplies the signal with a one-bit delayed copy and integrates; positive output means 1, negative means 0
   C. It uses a Viterbi equalizer
   D. It takes the FFT of each bit
   Answer: B. Same phase in consecutive bits gives positive output (1); opposite phase gives negative (0). (Key point: DPSK detection)

3. Which property holds for a maximal-length PN sequence from an m-stage LFSR?
   A. Period 2^m with equal 1s and 0s
   B. Autocorrelation 1 at all shifts
   C. Period m
   D. Period 2^m - 1, with one more 1 than 0s and autocorrelation -1/N off-peak
   Answer: D. m-sequences are balanced (1s exceed 0s by one), follow the run property, and have a sharp two-valued autocorrelation, which is why they suit spreading and synchronization. (Key point: m-sequence)

## Related in Wireless Communication

- [Spread spectrum and DSSS transmitter/receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspread-spectrum-dsss-tx-rx) — Wireless Communication, chapter 4
- [OQPSK transmitter/receiver and π/4-QPSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aoqpsk-pi4-qpsk) — Wireless Communication, chapter 4
- [OFDM transmitter and receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aofdm-transmitter-receiver) — Wireless Communication, chapter 4, asked 5×
- [Digital vs analog modulation; GMSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adigital-modulation-gmsk) — Wireless Communication, chapter 4
- [MSK modulation and DSSS](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amsk-dsss) — Wireless Communication, chapter 4

## Related in other subjects

- [Stereo FM transmitter and receiver; output of mono receiver](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Astereo-fm-mono-receiver) — Communication Systems, chapter 3
- [Why DPCM over PCM; DPCM transmitter and receiver](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adpcm-preferred-transmitter-receiver) — Communication Systems, chapter 4, asked 2×
- [Noise coupling mechanisms with pseudo impedance](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Anc-pseudo-impedance) — Instrumentation II, chapter 6
- [Map sequence diagram to pseudo code](https://www.bctengineer.com/question.md?key=semester_6%2Fobject_oriented_analysis_and_design%3Aorder-model-mapping-pseudocode) — Object Oriented Analysis and Design, chapter 4