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an air-substrate thickness of about 5% of the wavelength of the center operating frequency When the patch s aspect ratio and desired operating frequency are xed, this lowering in resonant frequency corresponds to an antenna size reduction of about 54% Since the lengthening of the effective patch s surface current paths is due to the additional downward paths in the added rims, which is different from that of the meandered designs [1, 6], a relatively very small perturbation on the excited surface current distribution in the radiating patch is expected This implies that it is possible for the radiation characteristics of this compact design to be as good as those of a corresponding conventional patch antenna with a planar radiating patch Prototypes of this compact design have been successfully implemented [12] The planar or top portion of the inverted U-shaped radiating patch is square and has a side length L.



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The two downward rims are identical and are added at the two radiating edges of the top patch The downward rims have a length of u, which is smaller than the air-substrate thickness h Centered below the inverted U-shaped patch is an H-shaped coupling slot cut in the ground plane of a microwave substrate of thickness 08 mm and relative permittivity 44 On the other side of the ground plane, a 50microstrip feed line for feeding the inverted U-shaped patch through the H-shaped coupling slot is printed The H-shaped coupling slot has a central arm of dimensions 1 mm S and two side arms of dimensions 1 mm 2Sh Compared to a conventional narrow rectangular coupling slot, the use of an H-shaped coupling slot can reduce the antenna s backward radiation.

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For the proposed design with various rim lengths, good impedance matching can be obtained by selecting proper values of S, Sh , and the tuning-stub length t of the 50- microstrip feed line Figure 225 shows the measured return loss for constructed prototypes (antennas 1 3) and a reference antenna (a design without downward rims) The top square patch had a side length of 46 mm, and the air-substrate thickness was chosen to be.

The subject of this section is maximum likelihood estimation of parameters of expectation models from independent Poisson distributed observations. Suppose that w = (w1 . . W N ) is the vector of observations and 8 = (0, . . . . ~ the vector of unknown parameters. Then, the log-probability function of the observations is defined by (3.43):

(31.42)

(21)

Call and session arrivals are generated following a Poisson process [9], and mapped onto the appropriate QoS pro les [7], depending on the type of tra c carried. Circuit-switched (CS) speech and video calls are held for an exponentially distributed service time, and their inter-arrival periods follow exactly the same type of distribution [9]. Packetswitched services are implemented as an ON/OFF process with truncated distributions [11]. The duration of the ON period depends mainly on the allocated bit rate and object size, which is modelled di erently depending on the application carried [12]. Di erent distributions are also used to model the related OFF time behaviors and session lengths. The utilised tra c models and the adopted tra c mix (in share of calls) in the case study presented in Section 7.1.2.8 are listed in Table 7.3. All calls/sessions (generated at the beginning of each simulation) are subsequently processed (played back) taking into account the corresponding arrival times, service activities and priorities, hence the name virtual time simulator. 7.1.2.3 Path loss generator

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