On a Fast p-ary m-Sequence Transform

m-Sequences have been used widely in many applications, but the corresponding computation of the correlation-detection is overwhelming N2 operations, where N is the length of the m-sequence, such that it is unpractical. In this paper, a transform from p-ary m-sequence matrices to generalized Hadamard matrices is developed; and then by the fast generalized Hadamard matrices transform, a fast p-ary m-sequence transform is developed. The results show that the computation can be dramatically reduced from N2 to Nlog pN operations, so the fast p-ary m-sequence transform could enable a rapid correlation-detection at the receiver.

Two families of Niho sequences having four-valued cross correlation with m-sequences Dedicated to Professor Yingbo Zhang on the Occasion of His 70th Birthday

For two odd integers m and s with 1≤s < m and gcd(m, s) = 1, let h satisfy h(2~s-1) ≡1(mod 2~m+ 1) and d =(h + 1)(2~m-1) + 1. The cross correlation function between a binary m-sequence of period 22~m-1 and its d-decimation sequence is proved to take four values, and the correlation distribution is completely determined. Let n be an even integer and k be an integer with 1≤k≤n/2. For an odd prime p and a p-ary m-sequence {s(t)} of period p^n-1, define u(t) =∑(p^k-1)/2 i=0 s(d_it), where d_i = ip^(n/2) + p^k-i and i = 0, 1,...,(p^k-1)/2. It is proved that the cross correlation function between {u(t)} and {s(t)} is three-valued or four-valued depending on whether k is equal to n/2 or not, and the distribution is also determined.

M-Sequence for Reducing Peak-to-Average Power Ratio in PTS-OFDM Systems

A sub-optimum m-sequence method for reducing PAR distribution inPTS-OFDM is proposed in the pa- per. In order to reduce thecalculation load introduced by optimum PTS method, m-sequence offinding the optimum side information can be utilized, which will notbring very heavy burden to the OFDM system since the cal- culationcomplexity is determined mainly by the number of IDFT at the cost ofPAR distribution performance of OFDM system.

Transmit-reference UWB system based on m-sequence codes

In this article, a novel transmit-reference （TR） signaling scheme is proposed for ultra-wideband （UWB） system, where by invoking m-sequence codes the reference and data pulses can be transmitted side by side to increase the data rate. This structure enables demodulation with a simple and practical autocorrelation receiver despite existence of severe inter-pulse interference （IPI） To evaluate detection performance of the new designs, closed-form expression for bit error probability （BRP） is theoretically derived and simulation results confirm the analytical results. In addition, the proposed scheme can be extended to M-ary systems to further improve the data rate and power efficiency.

ANALYSIS OF SPECTRAL PHASE ENCODING OCDMA SYSTEM WITH PSEUDORANDOM CODING

Multiple access interference (MAI) is the most serious interference in spectral phase encoding optical code division multiple access (SPE OCDMA) systems. This paper focuses on the behavior of MAI in SPE OCDMA systems with pseudorandom coding. The statistical expectation of multi access interference (MAI) is derived and plotted. The results confirm that MAI can be suppressed effectively by pseudorandom coding with m sequences.

An input signal used in process identification - chaos sequence

The sequences which consist of any segment of a chaos sequence are called asC-sequences. These sequences could be used as a kind of input signals to replace M-sequences in theprocess identification. This substitution is theoretically proved to be feasible. InverseC-sequences are created in a way similar to inverse M-sequences to solve the problem thatC-sequences have non-ideal balance property, that is, the numbers of '0' and '1' are unequal.Besides its good pseudo-random property, the sequences have other advantages such as easy togenerate, varieties of the segment and adjustable cycle time.

Recent developments in optimal experimental designs for functional magnetic resonance imaging

Functional magnetic resonance imaging(fMRI)is one of the leading brain mapping technologies for studying brain activity in response to mental stimuli.For neuroimaging studies utilizing this pioneering technology,there is a great demand of high-quality experimental designs that help to collect informative data to make precise and valid inference about brain functions.This paper provides a survey on recent developments in experimental designs for fMRI studies.We briefly introduce some analytical and computational tools for obtaining good designs based on a specified design selection criterion.Research results about some commonly considered designs such as blocked designs,and m-sequences are also discussed.Moreover,we present a recently proposed new type of fMRI designs that can be constructed using a certain type of Hadamard matrices.Under certain assumptions,these designs can be shown to be statistically optimal.Some future research directions in design of fMRI experiments are also discussed.

SELECTION OF THE LINEAR COMBINING VECTOR G OF THE GENERALIZED SELF-SHRINKING GENERATORS

Given an m-sequence, the main factor influencing the least period of the Generalized Self-Shrinking （GSS） sequence is the selection of the linear combining vector G. Based on the calculation of the minimal polynomial ofL GSS sequences and the comparison of their degrees, an algorithm for selecting the linear combining vector G is presented, which is simple to understand, to implement and to prove. By using this method, much more than 2^L-l linear combining vectors G of the desired properties will be resulted. Thus in the practical application the linear combining vector G can be chosen with great arbitrariness. Additionally, this algorithm can be extended to any finite field easily.

Pseudo-randomness of the fourth class of GSS sequences

This paper discusses pseudo-randomness of a periodic sequence, named the fourth class of GSS sequence. We get the following results: ① Its least period always reaches the maximum (that is, 2n-1). ② Its least period and linear complexity keep robust under single-symbol-substitution. ③ It has good low-degree-auto-correlation feature. ④ It has good short-length-run-distribution.

Reconstruction of Antenna Radiation Pattern Based on Compressed Sensing

The measurement of the far-field radiation pattern is an important factor in describing the character-istics of the antenna.The measurement process is time consuming and expensive.Therefore,this paper proposes a novel method to reduce the number of samples required for radiation pattern measurement by adopting com-pressed sensing theory.This method reconstructs the radiation pattern from data measured by a few sensors,and the positions of these sensors are generated via the m-sequence.Simulation results demonstrate that the proposed algorithm can effectively reconstruct the complete radiation pattern by using the 50%samples.