The mappings from independent binary variables to quadrature amplitude modulation (QAM) symbols are developed. Based the proposed mappings and the existing binary mutually uncorrelated complementary sequence sets (MUCSSs), a construction producing QAM periodic complementary sequence sets (PCSSs) is presented. The resultant QAM PCSSs have the same numbers and periods of sub-sequences as the binary MUCSSs employed, and the family size of new sequence sets is increased with exponent of periods of sub-sequences. The proposed QAM PCSSs can be applied to CDMA or OFDM communication systems so as to suppress multiple access interference (MAI) or to reduce peak-to-mean envelope power ratio (PMEPR), respectively.

In a direct-sequence spread spectrum communication system, its multiple access interference, security and user number are mainly decided by correlation, linear span and family size of spreading sequences employed by such a system, respectively. In this letter, based on several families of the known sequences, a method for improving their linear span and family sizes is presented. It is worthy of mentioning that although the number of the proposed sequences with linear span not less than that of the known sequences is enormously increased, the former's correlation distribution is the same as the latter's one. In addition, the proposed sequences include No sequences and the known sequences mentioned above as special cases.

In communication systems, ZCZ sequences and perfect sequences play important roles in removing multiple-access interference (MAI) and synchronization, respectively. Based on an uncorrelated polyphase base sequence set, a novel construction method, which can produce mutually orthogonal (MO) ZCZ polyphase sequence (PS) sets and perfect PSs, is presented. The obtained ZCZ PSs of each set are of ideal periodic cross-correlation functions (PCCFs), in other words, the PCCFs between such two different sequences vanishes, and the sequences between different sets are orthogonal. On the other hand, the proposed perfect PSs include Frank perfect PSs as a special case and the family size of the former is quite larger than that of the latter.

In this paper, for odd n and any k with gcd(n,k) = 1, new binary sequence families Sk of period 2n-1 are constructed. These families have maximum correlation , family size 22n+2n+1 and maximum linear span . The correlation distribution of Sk is completely determined as well. Compared with the modified Gold codes with the same family size, the proposed families have the same period and correlation properties, but larger linear span. As good candidates with low correlation and large family size, the new families contain the Gold sequences and the Gold-like sequences. Furthermore, Sk includes a subfamily which has the same period, correlation distribution, family size and linear span as the family So(2) recently constructed by Yu and Gong. In particular, when k=1, is exactly So(2).

In direct-sequence code-division multiple-access (DS-CDMA) communication systems and direct-sequence ultra wideband (DS-UWB) radios, sequences with low correlation and large family size are important for reducing multiple access interference (MAI) and accepting more active users, respectively. In this paper, a new collection of families of sequences of length pn-1, which includes three constructions, is proposed. The maximum number of cyclically distinct families without GMW sequences in each construction is , where p is a prime number, n is an even number, and n=2m, and these sequences can be binary or polyphase depending upon choice of the parameter p. In Construction I, there are pn distinct sequences within each family and the new sequences have at most d+2 nontrivial periodic correlation {-pm-1,-1,pm-1,2pm-1,,dpm-1}. In Construction II, the new sequences have large family size p2n and possibly take the nontrivial correlation values in {-pm-1,-1,pm-1,2pm-1,,(3d-4)pm-1}. In Construction III, the new sequences possess the largest family size p(d-1)n and have at most 2d correlation levels {-pm-1,-1,pm-1,2pm-1,,(2d-2)pm-1}. Three constructions are near-optimal with respect to the Welch bound because the values of their Welch-Ratios are moderate, WR d, WR 3d-4 and WR 2d-2, respectively. Each family in Constructions I, II and III contains a GMW sequence. In addition, Helleseth sequences and Niho sequences are special cases in Constructions I and III, and their restriction conditions to the integers m and n, pm≠ 2(mod 3) and n≡ 0 (mod 4), respectively, are removed in our sequences. Our sequences in Construction III include the sequences with Niho type decimation 32m-2, too. Finally, some open questions are pointed out and an example that illustrates the performance of these sequences is given.