Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Wireless communications, advanced radar and sonar systems, and security systems for Internet transactions are contemporary examples of systems that employ digital signals to transmit information. This volume affords comprehensive, up-to-date treatment of the methodologies and application areas throughout the range of digital communication where individual signals, and sets of signals, with favorable correlation properties play a central role. Some application areas covered include Code Division Multiple Access (CDMA) signals such as those in use for cell-phone communication; digital systems for coded radar and sonar signals; and methods for secure authentication and stream cipher cryptology. The authors provide the necessary mathematical background to explain how the signals are generated and to show how the signals satisfy the appropriate correlation constraints.
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General Properties of Correlation I
Applications of Correlation to the Communication
Feedback Shift Register Sequences
Randomness Measurements and m Sequences
Transforms of Sequences and Functions
Cyclic Difference Sets and Binary Sequences with
2-level autocorrelation sequences 2-tuple balance property 5-term sequence Algorithm autocorrelation function bent function binary sequence boolean functions Chapter characteristic polynomial column compute constant-on-cosets construction coset leaders modulo Costas array crosscorrelation cyclic difference set cyclotomic cosets decimation defined Definition denoted elements are given equal equivalent Example exponents Figure finite field function from F2 GF(p GF(q Gold-pair Golomb Gong Hadamard difference sets Hadamard matrix Hadamard transform hyperoval sequences IEEE Trans interleaved sequence interleaved structure irreducible polynomial Lemma length Let f(x LFSR implementation LFSR sequences linear span matrix minimal polynomial modulo multiple nonlinearity nonzero notation Note orthogonal positive integer prime primitive element primitive polynomial Proof quadratic residue sequence randomness realizable pairs result satisfies Section sequence of period sequence over F shift register sequences shift sequence shift-distinct signal set spanning ruler Table Tr(x trace function trace representation trinomial values vectors WG sequences