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example, one common way to estimate the channel uses pilot-symbol-assisted modulation (PSAM) [143; 144, Sect. 10.3.2], which periodically inserts pilots into the stream of data symbols to extract the channel-induced fading. Estimation error (due to additive noise as well as wireless channel variation/decorrelation over time) will cause the channel fading extracted from the pilot symbols to differ from the actual fading affecting the data symbols, thereby inducing a performance degradation. The effects of channel estimation error or channel decorrelation on the performance of diversity systems has long been of interest. These previous studies focused on MRC receivers over Rayleigh fading channels [32,145 148], postdetection EGC receivers over fast Rician fading channels [149,150], SC receivers over Rayleigh [151] and Nakagami-m [152] fading channels, and SSC receivers over Nakagami-m fading channels [123]. In this section, we brie y summarize the work on the impact of channel estimation error or channel decorrelation on the performance of diversity systems. 9.10.1 Maximal-Ratio Combining



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On the other hand, the variance is the same as for a pure squeezed state: ( E )2 = , |E 2 E 2 | , = 0, |E 2 E 2 |0,

(Continued )

The same holds for the covariance matrix Note that these results are independent of the manner in which one would de ne the squeezed states, | ,

(29)

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10214 A General De nition of Squeezing One can now give a general de nition of squeezing with respect to a pair of quantum observables A and B with commutator [A, B] = iC = 0 When variances / are calculated in a generic state, one obtains from Cauchy Schwarz inequality A B v 1 | C | Now a state will be called squeezed (with respect to the pair (A, B)) 2 if ( A)2 (or ( B)2 ) < 1 | C | A state will be called ideally squeezed (with respect to 2 the pair (A, B)) if the equality A B = 1 | C | is reached together with ( A)2 (or 2 ( B)2 ) < 1 | C | Hence, the class of ideally squeezed states contains the set of pure 2 squeezed states 10215 Squeezing the Uncertainties To conclude this section, let us brie y explain the interest in squeezed states in various applications, particularly in the coding and transmission of information through optical devices From the above study of the electric eld, Glauber (standard) optical coherent states have, in the phase quadrature plane, circularly symmetric uncertainty regions, so the uncertainty relation dictates some minimum noise amplitudes, for instance, for the amplitude and phase (Figure 101) A further reduction in amplitude noise is possible only by squeezing the uncertainty region, reducing its width in the amplitude, that is, radial, direction while increasing it in the orthogonal, that is, angular or phase, direction, so that the phase uncertainty is increased Such light is called amplitude-squeezed (Figure 102) Conversely, phase-squeezed light (Figure 103) has decreased phase uctuations at the expense of increased amplitude uctuations There is also the so-called squeezed vacuum, where the center of the uncertainty region (corresponding to the average amplitude) is at the origin of the coordinate system, and the uctuations are reduced in some direction The mean photon number is larger than zero in this case; a squeezed vacuum is a vacuum only in the sense that the average amplitude (but.

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Table 22 (Continued )

Frame Relay -

Fig 101 Coherent light in the plane of phase quadratures The uncertainty region around one point of the plane is circularly symmetric

Fig 103 Phase-squeezed light in the plane of phase quadratures The uncertainty ellipse is stretched in the radial direction

not the average photon number) is zero For example, an optical parametric ampli er with a vacuum input can generate a squeezed vacuum with a reduction in the noise of one quadrature components on the order of 10 dB In summary, the main feature of the squeezed states lies in the fact that they offer the opportunity of deforming (squeezing!) in a certain direction the circle of quantum uncertainty that so becomes an uncertainty ellipse Hence, they provide a way of reducing the quantum noise for one of the two quadratures

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obtained by putting the FAN5093 into E*-mode. When the Droop pin is pulled to the 5V BYPASS voltage, the " A phase of the FAN5093 IS completly turned off, reducing in half the amount of gate charge power being consumed. E*-mode can be implemented with the circuit shown in Figure 3.

We have seen that squeezed states are obtained by forcing two-photon processes with time-dependent classical sources (from this the appellation two-photon coherent

Fig 102 Amplitude-squeezed light in the plane of phase quadratures The uncertainty ellipse is stretched in the angular direction

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states) The most general form of the corresponding Hamiltonian reads H = a a + 1 2 + f 2 (t) a + f 2 (t) a 2 + f 1 (t) a + f 1 (t) a

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