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Figure 19.3 Capacity vs receiver velocity for EGC for different antenna patterns A( , ). N = 4, 4 4 rake, G = 256, t = s = 0, Y0 = 2, L = 4, SNR = (20 0 /alpha mean) 1 .
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Figure 19.4 Capacity vs processing gain for EGC. a, vrec = 200 km/h, b, vrec = 150 km/h, c, vrec = 100 km/h; d, vrec = 50 km/h. Solid line: 4 4 rake; dashed line: 4 1 rake; A real antenna pattern of circular array at base station; B, 3 dB aproximation ( 3dB = 30 ) of the real antenna pattern; c = 1; N = 4, s = t = 0, Y0 = 2, L = 4, SNR = (20* 0 /alpha mean) 1 . Figure 19.5 represents the same results as a function of the receiver velocity. The system sensitivity function de ned by Equation (19.38) is shown in Figure 19.6. Sensitivity equal to 1 means that all capacity has been lost due to imperfections. Figure 19.6 demonstrates that very high values for the system sensitivity, even in the range close to 0.9, can be expected if a large number of users (low data rate corresponding to high G) are in the network. In this section we have presented a systematic analytical framework for the capacity evaluation of an advanced CDMA network. This approach provides a relatively simple way to specify the required quality of a number of system components. This includes multiple access interference canceller and rake receiver, taking into account all their imperfections. The
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Figure 19.5 Capacity vs the receiver velocity for EGC; solid lines, 4 4 rake; dashed lines, 4 1 rake. A, real antenna; B, 3 dB approximation of the real antenna. c = 1; N = 4, t = s = 0, Y0 = 2, L = 4, SNR = (20 0 /alpha mean) 1 . (a) a, G = 256; b, G = 160; (b) a, G = 80; b, G = 48; c, G = 40. system performance measure is the network sensitivity function representing the relative losses in capacity due to all imperfections in the system implementation. Some numerical examples are presented for illustration purposes. These results are obtained for a channel with double exponential (space and delay) pro le. It was shown that for the receiver velocity 100 200 km/h as much as 70 90 % of the system capacity can be lost due to the imperfections of the three-dimensional rake receiver and interference cancellation operation. variety of results are presented for different channel decay factor, fading rate and number of rake ngers. In general, under ideal conditions, the system capacity is increased if the number of ngers is increased. At the same time one should be aware that the system sensitivity
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Figure 19.6 Sensitivity vs processing gain for EGC. a, vrec = 200 km/h; b, vrec = 150 km/h; c, vrec = 100 km/h; d, vrec = 50 km/h. Solid line, 4 4 Rake; dashed line; 4 1 rake. A, real antenna pattern of circular array at base station; B, 3 dB aproximation ( 3dB = 30 ) of the real antenna pattern. c = 1; N = 4, s = t = 0, Y0 = 2, L = 4, SNR = (20 0 /alpha mean) 1 . is also increased if the fading rate and number of rake ngers are higher. The results and methodology presented in this section offer enough tools and data for the careful choice of the system parameters in realistic environments which are characterized by imperfections.
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19.2 CAPACITY OF AD HOC NETWORKS In this section we now discuss the capacity of wireless networks. The discussion is based on concepts presented in References [32, 33]. In an ad hoc network, it is supposed that n nodes are located in a region of area 1 m2 . Each node can transmit at W b/s over a common wireless channel. The channel in general may be broken up into several subchannels of capacity W1 , W2 , . . . , W M b/s. This will be immaterial for the nal results as long M as m=1 Wm = W . Packets are sent from node to node in a multihop fashion until they reach their nal destination. They can be buffered at intermediate nodes while awaiting transmission. Owing to spatial separation, several nodes can make wireless transmissions simultaneously, provided there is no excessive interference from others. In the sequel we will discuss the conditions under which a wireless transmission over a subchannel is received successfully by its intended recipient. Two types of networks are considered, Arbitrary networks, where the node locations, destinations of sources, and traf c demands, are all arbitrary, and Random Networks, where the nodes and their destinations are randomly chosen.
19.2.1 Arbitrary networks In the arbitrary setting we suppose that n nodes are arbitrarily located in a disk of unit area in the plane. Each node chooses an arbitrary destination to which it wishes to send traf c at