We develop a novel construction method for n-dimensional Hilbert space-filling curves. The construction method includes four steps: block allocation, Gray permutation, coordinate transformation and recursive construction. We use the tensor product theory to formulate the method. An n-dimensional Hilbert space-filling curve of 2r elements on each dimension is specified as a permutation which rearranges 2rn data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing an n-dimensional Hilbert space-filling curve. The tensor product formulation of n-dimensional Hilbert space-filling curves uses stride permutation, reverse permutation, and Gray permutation. We present both recursive and iterative tensor product formulas of n-dimensional Hilbert space-filling curves. The tensor product formulas are directly translated into computer programs which can be used in various applications. The process of program generation is explained in the paper.

The purpose of the paper is to show that boundary implication results hold for complex-valued uncertain linear time-delay systems. The results are derived by the Lambert W function and yield tractable robust stability criteria for simultaneously triangularizable linear time-delay systems. The setting is similar to a recently reported extreme-point result, but the assumed uncertainty sets can be much more free in shape.

In the centralized polling mode in IEEE 802.16e, a base station (BS) polls mobile stations (MSs) for bandwidth reservation in one of three polling modes; unicast, multicast, or broadcast pollings. In unicast polling, the BS polls each individual MS to allow to transmit a bandwidth request packet. This paper presents an analytical model for the unicast polling of bandwidth request in IEEE 802.16e networks over Gilbert-Elliot error channel. We derive the probability distribution for the delay of bandwidth requests due to wireless transmission errors and find the loss probability of request packets due to finite retransmission attempts. By using the delay distribution and the loss probability, we optimize the number of polling slots within a frame and the maximum retransmission number while satisfying QoS on the total loss probability which combines two losses: packet loss due to the excess of maximum retransmission and delay outage loss due to the maximum tolerable delay bound. In addition, we obtain the utilization of polling slots, which is defined as the ratio of the number of polling slots used for the MS's successful transmission to the total number of polling slots used by the MS over a long run time. Analysis results are shown to well match with simulation results. Numerical results give examples of the optimal number of polling slots within a frame and the optimal maximum retransmission number depending on delay bounds, the number of MSs, and the channel conditions.

In this paper, we analyze the robustness for low-density parity-check (LDPC) codes over the Gilbert-Elliott (GE) channel. For this purpose we propose a density evolution method for the case where LDPC decoder uses the mismatched parameters for the GE channel. Using this method, we derive the region of tuples of true parameters and mismatched decoding parameters for the GE channel, where the decoding error probability approaches asymptotically to zero.

Point Pattern Matching (PPM) is an essential problem in many image analysis and computer vision tasks. This paper presents a two-stage algorithm for PPM problem using ellipse fitting and dual Hilbert scans. In the first matching stage, transformation parameters are coarsely estimated by using four node points of ellipses which are fitted by Weighted Least Square Fitting (WLSF). Then, Hilbert scans are used in two aspects of the second matching stage: it is applied to the similarity measure and it is also used for search space reduction. The similarity measure named Hilbert Scanning Distance (HSD) can be computed fast by converting the 2-D coordinates of 2-D points into 1-D space information using Hilbert scan. On the other hand, the N-D search space can be converted to a 1-D search space sequence by N-D Hilbert Scan and an efficient search strategy is proposed on the 1-D search space sequence. In the experiments, we use both simulated point set data and real fingerprint images to evaluate the performance of our algorithm, and our algorithm gives satisfying results both in accuracy and efficiency.

The N-dimensional (N-D) Hilbert curve is a one-to-one mapping between N-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spatial relationship of the N-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, all the sides of the scanned region must have the same size and the length must be a power of two, which limits the application of the Hilbert scan greatly. Thus in order to remove these constraints and improve the Hilbert scan for general application, a nonrecursive N-D Pseudo-Hilbert scan algorithm based on two look-up tables is proposed in this paper. The merit of the proposed algorithm is that implementation is much easier than the original one while preserving the original characteristics. The experimental results indicate that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points, and it also shows the competitive performance of the Pseudo-Hilbert scan in comparison with other common scan techniques. We believe that this novel scan technique undoubtedly leads to many new applications in those areas can benefit from reducing the dimensionality of the problem.

A low-voltage and low-power RF mixer for WCDMA applications is presented. The paper presents a novel topology mixer that leads to a better performance in terms of isolation and power consumption for low supply voltage. The measuring results of the proposed mixer achieve: 7 dB power conversion gain, 10.4 dB double side band (DSB) noise figure, -2 dBm input third-order intercept point (IIP3), and the total dc power consumption of this mixer including output buffers is 2.2 mW from a 1 V supply voltage. The current output buffer is about 1.96 mW, the excellent LO-RF, LO-IF and RF-IF isolation achieved up to 49 dB, 39.5 dB and 57.3 dB, respectively.

As a fundamental building block of multirate systems, the downsampler, also known as the decimator, is a periodically time-varying linear system. An eigensignal of the downsampler is defined to be an input signal which appears at the output unaltered or scaled by a non-zero coefficient. In this paper, the eigensignals are studied and characterized in the time and z domains. The time-domain characterization is carried out using number theoretic principles, while the one-sided z-transform and Lambert-form series are used for the transform-domain characterization. Examples of non-trivial eigensignals are provided. These include the special classes of multiplicative and completely multiplicative eigensignals. Moreover, the locus of poles of eigensignals with rational z transforms are identified.

There is an increasing requirement for supporting complex multidimensional queries in Peer-to-Peer systems. In the centralized spatial database world, R-Trees and its variant structures are widely accepted due to their capabilities to manage complex multidimensional queries. In this paper, we propose a new multidimensional indexing structure for P2P systems, called Distributed Hilbert R-Trees (DHR-Trees), in which peers organize themselves into an overlay network, dynamically maintain routing tables with region information and collaboratively execute complex multidimensional queries, such as range query and k-nearest neighbors query, efficiently. DHR-Trees has similar topology to the P-Trees P2P system. The peers' routing tables are enhanced with spatial region information, which allow multidimensional query predicates to be adapted into P2P systems with minor modification. The structure design and two major multidimensional query algorithms are presented. Our experimental results demonstrate that it performs well on range queries and k-nearest neighbors queries with multidimensional data set.

This paper presents the implementation of a 31-tap FIR Hilbert transform digital filter chip used in the digital-IF receivers, to confirm the effectiveness of our new design method. Our design method that we previously reported is based on a computation sharing multiplier using a new horizontal and vertical common subexpression techniques. A 31-tap FIR Hilbert transform digital filter was implemented and fabricated in 0.35 µm CMOS standard cell library. The chip's core contains approximately 33k transistors and occupies 0.86 mm2. The chip also has an operating speed of 70 MHz over. The implementation results show that the proposed Hilbert transformer has a smallest cost factor and so that is a high performance filter.

A fully integrated broadband up-conversion mixer with low power consumption is demonstrated on 90 nm CMOS technology in this paper. This mixer has a single-ended input and a multi-layer stacked Marchand balun is used for converting the differential output of the single-balanced mixer topology to a single-ended output. This balun employs inductive coupling between two metal layers and includes slotted shields to reduce substrate losses. The circuit size is 650 µm570 µm. At 22.1 GHz, the integrated mixer achieves a conversion gain of 2 dB with a maximum power dissipation of only 11.1 mW from a 1.2 V dc power supply at LO power of 5 dBm. Input referred 1-dB compression point is -14.8 dBm. The LO and RF return loss are better than 10 dB for frequencies between 20-26 GHz.

The 2-dimensional (2-D) Hilbert curve is a one-to-one mapping between 2-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spacial relationship of the 2-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, both sides of the scanned rectangle must have same size and each size must be a power of two, which limits the application of the Hilbert scan greatly. In this paper, a Pseudo-Hilbert scan algorithm based on two look-up tables is proposed. The proposed method improves the Hilbert scan to be suitable for real-time processing and general application. The simulation indicates that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points. It also shows competitive performance of the Pseudo-Hilbert scan in comparison with other scan techniques.

An effective way to boost power gain without noise figure degradation in a cascode low noise amplifier (LNA) is demonstrated at 4 GHz using 0.35 µm SiGe HBT technology. This approach maintains the same current consumption because a low-pass π-type LC matching network is inserted in the inter-stage of a conventional cascode LNA. 5 dB gain enhancement with no noise figure degradation at 4 GHz is observed in the SiGe HBT LNA with inter-stage matching.

A 10-GHz sub-harmonic Gilbert mixer is demonstrated in this paper using the 0.35 µm SiGe BiCMOS technology. The time-delay when the sub-harmonic LO (Local Oscillator) stage generates sub-harmonic LO signals is compensated by using fully symmetrical multiplier pairs. High RF-to-IF isolation and sub-harmonic LO Gilbert cell with excellent frequency response can be achieved by the elimination of the time-delay. The SiGe BiCMOS sub-harmonic micromixer exhibits 17 dB conversion gain, -74 dB 2LO-to-RF isolation, IP1 dB of -20 dBm, and IIP3 of -10 dBm. The measured double sideband noise figure is 16 dB from 100-kHz to 100-MHz because the SiGe bipolar device has very low 1/f noise corner.

A 5.2 GHz 1 dB conversion gain, IP1 dB = -19 dBm and IIP3= -9 dBm double quadrature Gilbert downconversion mixer with polyphase filters is demonstrated by using 0.35 µm SiGe HBT technology. The image rejection ratio is better than 47 dB when LO=5.17 GHz and IF is in the range of 15 MHz to 45 MHz. The Gilbert downconverter has four-stage RC-CR IF polyphase filters for the image rejection. Polyphase filters are also used to generate LO and RF quadrature signals around 5 GHz in the double quadrature downconverter.

Binary sequences with good autocorrelation and crosscorrelation properties are widely used in signal processing. If the autocorrelation properties are optimum, then the sequences are called perfect. In this paper we show, that the calculation of the crosscorrelation between Gordon-Mills-Welch sequences and Dillon-Dobbertin sequences is related to the crosscorrelation of m-sequences and their decimations. Furthermore, we give an upper bound for the maximum crosscorrelation coefficient (in absolute value) for certain perfect sequences.

The Hilbert transformation together with empirical mode decomposition (EMD) produces Hilbert spectrum (HS) which is a fine-resolution time-frequency representation of any nonlinear and non-stationary signal. The EMD decomposes the mixture signal into some oscillatory components each one is called intrinsic mode function (IMF). Some modification of the conventional EMD is proposed here. The instantaneous frequency of every real valued IMF component is computed with Hilbert transformation. The HS is constructed by arranging the instantaneous frequency spectra of IMF components. The HS of the mixture signal is decomposed into subspaces corresponding to the component sources. The decomposition is performed by applying independent component analysis (ICA) and Kulback-Leibler divergence based K-means clustering on the selected number of bases derived from HS of the mixture. The time domain source signals are assembled by applying some post processing on the subspaces. We have produced experimental results using the proposed separation technique.

To find the best transformation between a "model" point set and an "image" point set is the main purpose of point pattern matching. The similarity measure plays a pivotal role and is used to determine the degree of resemblance between two objects. Although some well-known Hausdorff distance measures work well for this task, they are very computationally expensive and suffer from the noise points. In this paper, we propose a novel similarity measure using the Hilbert curve named Hilbert scanning distance (HSD) to resolve the problems. This method computes the distance measure in the one-dimensional (1-D) sequence instead of in the two-dimensional (2-D) space, which greatly reduces the computational complexity. By applying a threshold elimination function, large distance values caused by noise and position errors (e.g. those that occur with feature or edge extraction) are removed. The proposed algorithm has been applied to the task of matching edge maps with noise. The experimental results show that HSD can provide sufficient information for image matching within low computational complexity. We believe this sets a new direction for the research of point pattern recognition.

This paper demonstrates a small compact 5.7 GHz upconversion Gilbert micromixer using 0.35 µm SiGe HBT technology. A micromixer has a broadband matched single-ended input port. A passive LC current combiner is used to convert micromixer differential output into a single-ended output and doubles the output current for single-ended-input and single-ended-output applications. Thus, a truly balanced operation of a Gilbert upconversion mixer with a single-ended input and a single-ended output is achieved in this paper. The fully matched upconversion micromixer has conversion gain of -4 dB, OP1 dB of -9 dBm and OIP3 of 4 dBm when input IF=0.3 GHz, LO=5.4 GHz and output RF=5.7 GHz. The IF input return loss is better than 18 dB for frequencies up to 20 GHz while RF output return loss is 25 dB at 5.7 GHz. The supply voltage is 3.3 V and the current consumption is 4.6 mA. The die size is 0.90.9 mm2 with 3 integrated on-chip inductors.

Modulator output and fiber transmission characteristics of optical single sideband (SSB) modulations are analyzed under the assumption that SSB modulators are constructed using Mach-Zehnder (MZ) interferometers. The fiber input signal and the detected signal are derived theoretically for SSB modulation with and without an optical carrier. Optical SSB fiber transmission simulations show that the received signal waveform is degraded by harmonic components due to non-linear switching curve of MZ interferometer as a component of SSB modulators even if the Hilbert transformers is ideal for the definition. The optical SSB suppressed carrier is preferred to the SSB with an optical carrier from a viewpoint of waveform degradation.