Complementary Codes in Wireless Communication Systems
Summary
Complementary codes are sets of sequences that exhibit ideal correlation properties when combined, leading to zero or minimal sidelobes in their autocorrelation sums. In wireless communications, these codes underpin advanced modulation schemes and enable high-resolution signal separation in environments with multipath propagation. Families such as Golay complementary pairs and Z-complementary code sets (ZCCSs) have been deployed in orthogonal frequency-division multiplexing (OFDM), code-division multiple access (CDMA) and radar systems to mitigate inter-symbol interference, suppress Doppler-induced distortions and reduce peak-to-average power ratio (PAPR).
Construction techniques draw on algebraic and combinatorial methods, including generalised Boolean functions and Prouhet–Thue–Morse sequences, to generate flexible code lengths and set sizes. These developments have practical impact on multicarrier CDMA, quasi-synchronous systems and high-speed target detection, emphasising both theoretical bounds on correlation and real-world constraints such as power efficiency and Doppler resilience. The global importance of complementary codes is reflected in their integration into 5G and beyond, where spectral efficiency, robustness to fading and stringent power requirements converge.
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Complementary Codes in Wireless Communication Systems publication trend
The graph below shows the total number of articles in complementary codes in wireless communication systems across all publications each year (not limited to Nature Index journals).
Technical terms
Complementary code: A set of sequences whose autocorrelation sidelobes cancel when summed.
Golay complementary pair: Two sequences whose aperiodic autocorrelations sum to zero sidelobes.
Z-complementary code set (ZCCS): A collection of sequences with zero correlation in specified sidelobe zones.
Peak-to-average power ratio (PAPR): The ratio of the maximum power to the mean power of a signal waveform.
Orthogonal frequency-division multiplexing (OFDM): A multicarrier modulation technique dividing data across orthogonal subcarriers.
Quasi-synchronous CDMA (QS-CDMA): A CDMA system allowing limited time shifts while maintaining low cross-correlation.
References
- Z-Complementary Code Sets With Flexible Lengths From Generalized Boolean Functions. IEEE Access (2020).
- A Construction of Binary Golay Complementary Sets Based on Even-Shift Complementary Pairs. IEEE Access (2020).
- Spreading Sequence Design and Theoretical Limits for Quasisynchronous CDMA Systems. EURASIP Journal on Wireless Communications and Networking (2004).
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