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For the cases shown in Figures 9.22b and 9.22c, which usually occur in microcell environments for BS-MO-communications or for MO-MO-communications, the angular spread may become wide enough (up to 45 60 ) to decrease the ef ciency of the adaptive antenna. Thus, a dispersion of the radio environment results in the distortion of the antenna side-lobe levels at the base station [162], as well as in an increase in the correlation of fading at different antenna elements of the array [132]. The problem of fading correlations is studied in Reference [163]. It was shown that by deriving the relationships between AOA, beamwidth, and correlation of fading, larger element spacing is required to reduce the correlation, especially when the AOA is parallel to the array. A correlation coef cient of fading, between the various antenna elements, greater than 0.8 can cause signals at all elements to fade away simultaneously [164]. A detailed investigation of the effect of fading correlation on the performance of the adaptive arrays to combat fading was done in Reference [132]. It was shown that a correlation up to 0.5 causes little degradation of the antenna ef ciency, but a higher correlation decreases its performance signi cantly. However, the array is able to suppress interferences as independent fading is not required for interference suppression [132]. The aspect of AOA distribution as well as delay spread distribution for different land communication links will be analyzed in detail in the s 10 and 13. 9.4.4. Range Increase In typical land macrocell communication links with high base station antenna and low mobile antenna (see Figs. 9.22a and 9.22b), when angular spread is small enough, a MIMO system consisting of M and N-element antenna arrays at both ends of the link gives a link gain of GL MN with a diversity gain equal to NM (see Section 9.3). It means that both the physical M-element adaptive array and a multibeam (phased array) antenna provide an MN-fold increase in antenna gain. Even if only one antenna (either base station or mobile) is in the form of an array with M elements, the increase the will be in GL M times. In the case of low p p elevation antennas shown in Figure 9.22c, the link gain is GL M N 2 with a diversity gain of NM. If N is small and M is large, the gain will approach M. This capability of adaptive or multibeam antennas to increase the range of a 1=g communication link by the factor GL is used to reduce the number of base stations 2=g required to cover a given area by a factor of GL , where g is the propagation-loss exponent. From 5, g is set to be somewhere between 2 and 5. The physical adaptive array antenna also provides diversity gain, and for a given array size with spatial diversity, the diversity gain increases with angular spread and the fading correlation decreases, thus providing a greater range for the radio link. For the multibeam (phased array) antenna, however, the diversity gain is limited, as angular diversity provides only a small diversity gain. Another disadvantage of the multibeam antenna is that the antenna gain is limited by the angular spread. That is, the antenna cannot provide additional antenna gain when the beamwidth is less than the angular spread because smaller beamwidths exclude signal energy outside the beam.
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With an angular spread of a0 20 for a 10-element adaptive antenna, the range can be increased by a factor of 2 (with respect to the single element), whereas for the same 10-beam multibeam antenna, the increase is about 1.7 [165]. This difference increases with any increase in the number of adaptive antenna elements or beams in a multibeam antenna. For example, for 30-element antenna with an angular spread of a0 20 , the range increase is 2.5 times that of a single regular antenna, whereas for the same angular spread and number of beams, the range increase of the multibeam antenna will be by a factor of 1.7. Note that these results are valid only for the uplink, where the mobile user transmits information and the base station receives it [165]. For the downlink, as the downlink frequency is different from the uplink frequency [for FDMA, GSM (combination of FDMA and TDMA), IS-95, and IS-136 systems], the same adaptive array techniques cannot be used for transmission by the base station and reception by the mobile antenna. Here, the multibeam antenna can be used more effectively, but to achieve diversity gain, transmit diversity must be used or the handset vehicle must have multiple antennas [166]. Although these techniques may provide less gain on the downlink than on the uplink, this may be compensated for by the higher transmit power of the base station as compared to the handset vehicle. The results obtained in Reference [165] are valid for the uplink and for systems close to TDMA or its combinations with FDMA. In CDMA systems, the RAKE receiver provides three-time diversity, and different beams can be used for each output of the RAKE receiver. So, in CDMA the multibeam antenna gives the same range increase as the adaptive array antenna. As multibeam antennas require less complexity (with respect to weight and tracking), the multibeam antenna is preferable for CDMA systems, whereas an adaptive array antenna may be preferable for TDMA or GSM systems, particularly in environments with large angular spreads. 9.4.5. Reduction in Co-Channel Interference and Outage Probability In this section we will brie y consider the integration of an idealized adaptive antenna array into an existing cellular network and will compare it with the conventional omnidirectional base-station antenna following the well-known hexagonal cell topology, all details of which the reader can nd in References [91 94,167]. Let the cluster size be given in terms of the number of cells NC , which uses different frequencies compared to the wanted cell (i.e., the cell under service). This number (NC ) is related to the co-channel reuse factor Q D=Rcell by References [103,167]: NC Q2 =3 9:47
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where Rcell is the radius of a cell and D is the reuse distance, which de nes a range between cells allocated by the same frequency band. There is a limited number of NC cells that are possible in a hexagonal cellular network [103,167], that is, NC 3, 4, 7, 9, 12, . . .
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