Quaternary Spreading Codes and the S(2) Code in 3G-WCDMA

In Code Division Multiple Access (CDMA) cellular systems, multiple users share the same frequency band by using pseudorandom spreading codes to distinguish their signals at the base station. Professor Kumar was a pioneer in the development of quaternary spreading codes, which are well-suited for systems using Quaternary Phase-Shift Keying (QPSK)a widely adopted modulation format.

A major requirement for third-generation (3G) cellular networks was the availability of short spreading codes that could support a large number of simultaneous users. To address this, Professor Kumar co-designed the S(2) quaternary spreading code, which includes over 16 million unique sequences a capacity far greater than that of similar binary code families.

This vast code set played a crucial role in the 3rd Generation Partnership Project (3GPP) adopting the S(2) code as the short scrambling code for the global 3G-WCDMA standard. The S(2) code has since been deployed in millions of mobile phones worldwide.

Reference

1. Kumar, et al.,"4-phase sequences with near-optimum correlation properties", IEEE Trans. On Information Theory 1992 (345 Google Scholar Citations (GSC)).

2. Kumar et al., "An upper bound for Weil exponential sums over Galois rings and applications", IEEE Trans. on Information Theory, 1995 (GSC: 191 ).

3. Kumar, et al., "Large families of quaternary sequences with low correlation", IEEE Trans. on Information Theory, March 1996, (GSC: 151).

4. 3GPP TS 25.213: (Release 18), V18.0.0, Spreading and modulation, (2024- 03), (see p. 33).

5. B. M. Popovic,"Quadriphase Spreading Codes in Code Division Multiple Access", US Patent No. 6,393,047 B1, May 21, 2002, (see pages 1-2).