---
title: "How CDMA works"
subject: "Data Communication"
chapter: 6
key: "semester_5/data_communication:cdma-working"
source: https://www.bctengineer.com/q/semester_5/data_communication/cdma-working
site: BCT Engineering
---

# How CDMA works

Data Communication · Chapter 6: Multiplexing and Spreading

- Asked in: 2078 Bhadra, 5 marks; 2071 Chaitra, 2 marks (asked 2 times)
- Video: [Code Division Multiple Access (CDMA)](https://www.youtube.com/watch?v=BkThmLtjQpE) — TutorialsPoint
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/cdma-working
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-6

## Question

Explain how CDMA works with example.

## Short answer

In CDMA, each station is assigned a unique orthogonal chip sequence. A bit 1 is sent as +code, 0 as -code, and silence as 0. The receiver recovers a station's data by taking the inner product of the received sum signal with that station's code, dividing by code length N.

## Answer

**Code Division Multiple Access (CDMA)** lets all stations use the whole bandwidth at the same time. Each station is assigned a unique **chip sequence (code)**, and the codes are mutually **orthogonal**. A bit is spread by its code before sending, and the receiver recovers one station's data by taking the inner product of the received sum with that station's code.

#### Principles
- Data 1 is sent as +code, data 0 as −code, and silence as 0.
- Orthogonal codes: inner product of two different codes is 0, and of a code with itself is N (code length).
- The channel adds the signals of all stations.
- To recover station X's data, multiply the total signal by X's code, add up, and divide by N: result +1 means bit 1, −1 means bit 0, 0 means silent.

#### Example (N = 4, Walsh codes)
A = [+1 +1 +1 +1], B = [+1 −1 +1 −1], C = [+1 +1 −1 −1], D = [+1 −1 −1 +1].

Let A send bit 1 (+1), B send bit 0 (−1), C silent (0), D send bit 1 (+1).

```text
 A*(+1) = +1 +1 +1 +1
 B*(-1) = -1 +1 -1 +1
 C*( 0) =  0  0  0  0
 D*(+1) = +1 -1 -1 +1
 Total  = +1 +1 -1 +3
```

Decoding the total [+1 +1 −1 +3]:
- A: (1+1−1+3)/4 = +1, so bit 1
- B: (1−1−1−3)/4 = −1, so bit 0
- C: (1+1+1−3)/4 = 0, so silent
- D: (1−1+1+3)/4 = +1, so bit 1

All four are recovered correctly. Used in IS-95 and 3G (WCDMA); close to DSSS in principle.

## Check yourself

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

1. What is the inner product of two different orthogonal codes?
   A. N
   B. 1
   C. 0
   D. -N
   Answer: C. Different orthogonal codes give 0, and a code with itself gives N. (Key point: Orthogonality)

2. How are data bits sent in CDMA?
   A. 1 as +code, 0 as -code, silence as 0
   B. 1 as -code
   C. 0 as +code
   D. Using frequencies
   Answer: A. Signs of the code carry the bit. (Key point: Bit encoding)

3. How is station X's bit recovered?
   A. Inner product of total signal with X's code, divided by N
   B. Add all signals
   C. Filter by frequency
   D. Multiply by a different code
   Answer: A. Other stations' contributions cancel to zero. (Key point: Decoding)

4. Total = [+1 +1 -1 +3]. What does station B = [+1 -1 +1 -1] give?
   A. +1
   B. -1
   C. 0
   D. +3
   Answer: B. (1 - 1 - 1 - 3)/4 = -1, so bit 0. (Key point: Example)