Quadriphase and 8-phase sequences with good autocorrelation properties are required in higher order digital modulation schemes, e.g., for channel estimation or synchronization. Since such sequences with perfect periodic autocorrelation function exist only for a few lengths, mismatched filtering is discussed. Mismatched filtering entirely suppresses all sidelobes of the correlation function at the expense of a slightly reduced signal-to-noise ratio (SNR). We present new construction methods for quadriphase and 8-phase sequences which exist for many lengths and exhibit significantly lower SNR losses than any other known sequences.

Time-discrete signals with good autocorrelation properties are used in various applications in communications engineering. From an implementation point of view, usually sequences with a small phase alphabet and a maximal energy efficiency, i.e., a uniform envelope, are most favorable. For this reason, known methods as well as several new construction techniques of binary and quadriphase sequences with optimal or best known autocorrelation properties are discussed in this correspondence. In many cases, the achievable correlation properties can be improved significantly if a single zero element per sequence is accepted. These "almost" binary and "almost" quadriphase sequences are considered as well. The optimality criteria used include the maximum absolute sidelobe and the merit factor of the periodic and the odd-periodic autocorrelation function, respectively. For sequence lengths of up to 44 in the binary case and up to 32 in the quadriphase case, the best known parameters obtained by computer search are compared with the constructed results.

Binary Alexis (1986) sequences are useful signals for fast start-up equalization, channel estimation, synchronization, or ranging. The aperiodic autocorrelation functions of Alexis sequences vanish in a broad window region when correlated using additional binary preamble and postamble sequences. Originally, Alexis sequences were found by computer search. Two methods are presented by which such sequences can be constructed for any length N=p/sup a/ and N=2(p/sup a/+1), where p, is an odd prime and a=1, 2, 3.

A new class of quadriphase sequences of length N=p/sup J/+1/spl equiv/2 mod 4(p odd prime, J=1,2,...) is presented. These almost-perfect sequences have a periodic autocorrelation function /spl Theta/ (/spl tau/) which vanishes for all /spl tau//spl ne/0mod (N/2).

Signals of two or more dimensions with ideal impulse-like periodic autocorrelation functions are used in higher-dimensional signal processing or in radar systems. Four synthesizing methods for perfect ternary arrays are presented. Based on known perfect binary and ternary sequences and arrays, many new perfect ternary arrays with increasing number of elements are constructed. New strong conditions for the existence of perfect arrays are developed. By combining these conditions with an advanced computer search, new ternary arrays are found. These new ternary arrays can be used as starting arrays to construct additional perfect ternary sequences and arrays.>