Let m ≥ 3 be an odd positive integer, n=2m and p be an odd prime. For the decimation factor $d=rac{(p^{m}+1)(p^{m}+p-1)}{p+1}$, the cross-correlation between the p-ary m-sequence {tr1n(αt)} and its all decimated sequences {tr1n(αdt+l)} is investigated, where 0 ≤ l < gcd(d,pn-1) and α is a primitive element of Fpn. It is shown that the cross-correlation function takes values in {-1,-1±ipm|i=1,2,…p}. The result presented in this paper settles a conjecture proposed by Kim et al. in the 2012 IEEE International Symposium on Information Theory Proceedings paper (pp.1014-1018), and also improves their result.

Let p be an odd prime and m be any positive integer. Assume that n=2m and e is a positive divisor of m with m/e being odd. For the decimation factor $d=rac{(p^{m}+1)^2}{2(p^e+1)}$, the cross-correlation between the p-ary m-sequence ${tr_1^n(alpha^i)}$ and its decimated sequence ${tr_1^n(alpha^{di})}$ is investigated. The value distribution of the correlation function is completely determined. The results in this paper generalize the previous results given by Choi, Luo and Sun et al., where they considered some special cases of the decimation factor d with a restriction that m is odd. Note that the integer m in this paper can be even or odd. Thus, the decimation factor d here is more flexible than the previous ones. Moreover, our method for determining the value distribution of the correlation function is different from those adopted by Luo and Sun et al. in that we do not need to calculate the third power sum of the correlation function, which is usually difficult to handle.

Let d=2pm-1 be the Niho decimation over $mathbb{F}_{p^{2m}}$ satisfying $gcd(d,p^{2m}-1)=3$, where m is an odd positive integer and p is a prime with p ≡ 2(mod 3). The cross-correlation function between the p-ary m-sequence of period p2m-1 and its every d-decimation sequence with short period $rac{p^{2m}-1}{3}$ is investigated. It is proved that for each d-decimation sequence, the cross-correlation function takes four values and the corresponding correlation distribution is completely determined. This extends the results of Niho and Helleseth for the case gcd(d, p2m-1)=1.

This letter deals with the time-domain estimation of time-varying channels in orthogonal frequency-division multiplexing (OFDM) systems. The general complex exponential basis expansion model (GCE-BEM) is used to capture the time variation of the channel within an OFDM block. The design criterion of optimal training for OFDM systems in time-varying channels is derived. This optimal training enables the complete elimination of the interference from data symbols and minimizes the noise effect on channel estimation. The design criterion can be used for both pilot symbol aided modulation (PASM) and superimposed training OFDM systems over time-varying channels.

A low complexity minimum mean squared error (MMSE) equalizer for orthogonal frequency division multiplexing (OFDM) systems over time-varying channels is presented. It uses a small matrix of dominant partial channel information and recursive calculation of matrix inverse to significantly reduce the complexity. Theoretical analysis and simulations results are provided to validate its significant performance or complexity advantages over the previously published MMSE equalizers.