移动通信工程第七章PPT课件

•
R c () E [ X 1 X 2 ] E [ Y 1 Y 2 ] 2 0 S ( f) c2 o fd sf (7.13)
•
R c ( s ) E [ X 1 Y 2 ] E [ Y 1 X 2 ] 2 0 S ( f) s2 if n d(f 7.14)
• are correlated, then E[X1X2] and E[X1Y2] are not necessarily zero. Consequently,
• it is first necessary to find the covariance matrix for these
• random variables, and then the characteristics of ψ(t) and ψ (t) can beintroduced.
• Hence ψ1(t) can be defined:
•
(t) arctan Y1
X1
• The terms X1 and Y1 of the signal s(t) are two independent Gaussian
• variables with zero mean and a variance of σ2. This means that:
• noise. Since the signals s1 and s2 shown in Eqs.four random variables—X1, Y1, X2, and Y2—then the following expressions
• of covariances can be derived from Eq. (7.12):
• time derivative of ψ(t), ψ・ (t) = dψ(t)/dt, is the random FM that is
• described in this chapter.
• Assume that aj(t) is the jth wave arrival, then s(t) represents the sum
• From Eq. (E 7.[9S ),1S th2 * e]f ollT oli wm i ng2 1 T exp rT T esss(ito)nss*( atre ob)tained:
• Rc(τ) = E[X1X2] = E[Y1Y2]
(7.10)
• •
Rs(τ) = E[X1Y2] Equations (7.10)
CHAPTER7 Received-Signal Phase Characteristics
• A signal s0(t) received at the mobile unit can be expressed:
•
s0(t) = m(t)s(t) (7.1)
• The long-term-fading factor m(x) is extracted from s0(t) and the resultant
•
E[X1Y1] = 0 (7.5)
•
E[X12] = E[Y12] = σ2 (7.6)
• But when two signals s1 = s(t) and s2 = s(t + τ), expressed
s1(t) = X1 + jY1 = r1ejψ1 (7.7)
• and
s2(t) = X2 + jY2 = r2ejψ2 (7.8)
• of all wave arrivals, as has been shown in Eq. (6.10):
•
s(t) = ∑a(t)=X1 + jY1 (7.3)
• where X1 and Y1 are as defined in Eqs. (6.11) and (6.12), respectively.
• Eq. (2.99):
• •
where
S(
f)
df
isE t[hse1s2 a*]v eraR g(e)p ow e rS th(aft)e liejsw d in thfe
(7.12) frequency
range
f,
• f + df. S( f) is often given in order to specify the spectrum of a given
=an−dE[(Y71.1X12)E ]h[s1 as2 * v] eR b(e)( e7n . 1S u1(sf))eedjw d infChap.
6
for
calculating
• the covariances of random variables. Also E[s1s*2] can be expressed as in
CONTENTS
• 7.1 Random Variables Related to Mobile-Radio Signals
• 7.2 Phase-Correlation Characteristics • 7.3 Characteristics of Random FM • 7.4 Click-Noise Characteristics • 7.5 Simulation Models
7.1.1Finding the covariance of random variables
• Since the ergodic process is always applied to random variables in the mobile-radio environment, then Eq. (2.80) can also be used here:
• can be expressed:
•
s(t) = r0ejψ(t) (7.2)
• where r0(t) and ψ(t) are the envelope and phase terms, respectively. The
• characteristics of r0(t) have been discussed in Chap. 6. The phase and