Orthogonal Pulsing Scheme

Waveform diversity can be used on the sequence of transmitted radar pulses to realize the above goal by suppressing the range foldover returns. In ordinary practice, a set of identical pulses are transmitted. To suppress returns due to range foldover, for example, individual pulses 

Keywords continuous wave radar linear frequency modulation noise radar noise  

Advances in Sensing with Security Applications, 215—242. 2006 Springer. Printed in the Netherlands. 

The process of detection can be performed by using different sensing technologies and different sensors. 

A single sensor usually has limited range and accuracy — especially in the cross-range direction. The use of bistatic ideas, where the transmit- 

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S. U. Pillai, B. Himed, K. Y. Li, Orthogonal Pulsing Schemes for Improved Target Detection in Space Based Radar, 2005 IEEE Aerospace Conference, Big Sky, MT, March 5-12, 2005. 

Fig. 1.4 Phase encoding scheme in three ween the rf pulses and before the acquisition of dimensions. Three pulsed gradients in ortho- the echo signal. In practice, the gradients are gonal directions are applied and are varied often applied simultaneously. The indices 1, 2 independently of each other (symbolized by the and 3 represent orthogonal directions with no diagonal line). The actual timing of the gradi- priority being given to a particular choice of ents is arbitrary provided they are placed bet- combinations.

The simplest double tuned filter can be constructed by a concatenation of two X-half filters and removal of redundant 180° pulse pairs (Fig. 17.4d) [22]. Alternatively, it can also be realized by keeping the 180° pulse pairs and adding short spin-lock periods (to dephase the 1H-13C magnetization which is orthogonal to the spin-lock axis, Fig. 17.4e) [23], or it is based on the gradient-purging scheme of Fig. 17.4b, resulting in the double filter shown in Fig. 17.4f [18]. 

A closely related technique can be used for multi-slice imaging (Fig. 6.2.7) [Fral]. The scheme of Fig. 6.2.5(c) is appended by further slice-selective 90° pulses with different centre frequencies, so that the magnetization of other slices is selected [Fral]. In this way, the otherwise necessary recycle delay can effectively be used for acquisition of additional slices. However, the contrast in each slice is affected by a different Ty weight, because is different for each slice. The technique can readily be adapted to line-scan imaging by applying successive slice-selective pulses in orthogonal gradients [Finl]. 

The final orthogonal format which we consider is binary pulse-position modulation (PPM/IM). In this scheme, each bit period is divided into two equal subintervals. If a 1(0) is transmitted, the pulse is caused to occur in the first (second) subinterval. A block diagram for one implementation of such a system... 

In the multiplexing scheme considered by Alt and Pleshko, rectangular voltage pulses with duty ratio 1/N and a common amplitude are applied to each of the N rows in succession. These row signals Fj, which may be called strobe signals, are mutually orthogonal and have identical rms values F, i.e.. 

The on-voltage given by Eq. (9) constitutes the upper limit, not only for the pulsed waveforms considered by Alt and Pleshko, but also for any multiplexed addressing scheme so defined. Thus, no other set of orthogonal strobe functions, such as sinusoids of different frequencies or Walsh functions of different sequencies, can lead to better performance. We will show next that this limit can be exceeded if the functional dependence of a ) is more general than in Eq. (8). 

A specific aspect of the ionization problem are the expansion coefficients Ci, i Ek,t) related to the electronic continua. Their dependence on the continuous variable Ek leads to a noncountably infinite set of differential equations. To arrive at a computationally manageable scheme, the continua have to be discretized. An ingenious discretization scheme, which proves particularly efficient in the present context, has been proposed by Bur key and Cantrell. The energy-dependent coefficients are expanded in terms of polynomials which are orthogonal with respect to the ionization cross section as weight function (see Ref. 24 for details). It has been shown that for pulses of short duration only a small number of expansion terms has to be considered, which renders this scheme very efficient for femtosecond PP applications. ... 

Our studies of non-canonical amino acids were motivated initially by an interest in making proteins with novel properties. Our interest broadened when our colleague Daniela Dieterich suggested that pulsed metabolic labeling of cellular proteins with non-canonical amino acids might provide a method for time-resolved analysis of protein synthesis in neurons. With Daniela and Erin Schuman, we developed this idea into the BONCAT (bio-orthogonal non-canonical amino acid tagging) method shown in Scheme 2 [33]. 

A scheme [2.15] is presented to follow the evolution of the density matrix in pulse experiments for a system of isolated spin 1 = 1 nuclei. In this case, it is convenient to express a t) in terms of an orthogonal basis set of nine [(2/ + 1) ] 3x3 matrices in an operator space. The choice of this complete basis set is not unique and varies according to the natme of the problem to be solved. A set in which the matrices are Hermitian is chosen so that the spin states represented by these matrices have real physical significance, and the matrices obey convenient conunutation relations with the operators in the Hamiltonian of interest. 

An interesting general NMR building block, referred to as perfect echo, has shown a renewed interest in the last years because the J(HH) effects generated during a spin-echo period can be efficiently refocused for a spin AX system (Eq. 5). Basically, it is a double spin-echo scheme separated by an orthogonal J-refocusing 90° pulse, with the interpulse delay set to A-Cl/ J(HH) (Fig. IIB) [89]. 

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