第三章 小尺度信道模型

• Cross Correlation of inphase/quad signal is Ar ,r (τ ) = PEθ [sin 2πf D τ ] = − Ar ,r (τ )
I Q n n I Q
• Autocorrelation of received signal is Ar (τ ) = ArI (τ ) cos(2πf cτ ) − ArI ,rQ (τ ) sin(2πf cτ )
• Random # of multipath components, each with
– – – – Random amplitude Random phase Random Doppler shift Random delay
• Random components change with time • Leads to time-varying channel impulse response
δ (τ − ξ )dξ = α (τ , t )e
− jφ (τ ,t )
Received Signal Characteristics
• Received signal consists of many multipath components • Amplitudes change slowly • Phases change rapidly
– Constructive and destructive addition of signal components – Amplitude fading of received signal (both wideband and narrowband signals)
Narrowband Model
• path delay for MP component currently observed
时变色散信道连续多径模型
c(τ , t ) = ∑ α n (t )e
n N (t ) − jφ n ( t )
δ (τ − τ n (t ))
⇓ c(τ , t ) = ∫ α (ξ , t )e
− jφ ( ξ , t )
−∞
时变色散信道离散多径模型 • Response of channel at t to impulse at t-τ :
c(τ , t ) = ∑ α n (t )e
n N (t ) − jφ n ( t )
δ (τ − τ n (t ))
n
φn (t ) = 2πf cτ n (t ) − 2π [ f c − f c′ + f D (t )]t − (φc − φc′ )
研究生《现代无线通信技术》课程
第三章 无线信道小尺度模型
余 华
华南理工大学电子与信息学院 2011年3月21日星期一
主要内容 无线信道模型 无线信道分类 无线信道统计模型 离散时间信道模型 Matlab信道仿真
小尺度模型
• 小尺度传播的主要效 应：
信号强度的快速变化 时变引起的多普勒频移 多径引起的延时扩展
′ j {2π (( f c − f c′ )t − f cτ )+(φc −φc )}
jφ
+ z(t )
信道延迟 收发端振荡器 频率随时间变 化的相对漂移 及多普勒频移
收发端振荡器初 始相位的差异
发送端振荡器频率(及其 漂移)与时延的共同效应
多谱勒频移
u (t )
(
e
j ( 2πf c t +φc )
• Assume delay spread maxm,n|τn(t)-τm(t)|<<1/B • Then u(t-τn(t)) ≈ u(t-τ) • Received signal given by
⎧ ⎡ N (t ) − jφ n ( t ) ⎤ ⎫ j 2πf c t r (t ) = ℜ⎨u (t )e ⎥⎬ ⎢ ∑ α n (t )e ⎣ n =0 ⎦⎭ ⎩
信号通过AWGN延迟信道的等价低通模型
u (t )
e
j ( 2πf c t +φc )
s (t )
r (t )
e
′ − j ( 2πf c′t +φc )
v(t )
s ( t ) = Re u ( t ) e = Re u ( t ) e
( (
j ( 2 πf c t +φ c )
) )
r (t ) = s (t − τ ) + n (t )
信号通过时变色散信道的等价低通模型
u (t )
h(τ ; t )
e
j ( 2πf c t +φc )
s (t )
r (t )
e
′ − j ( 2πf c′t +φc )
v(t )
c(τ ; t )
u (t )
∞ −∞ ∞
v(t )
r (t ) = (h * s )(t ) + n(t ) = ∫ h(τ , t ) s (t − τ )dτ + n(t ) v(t ) = (c * u )(t ) + z (t ) = ∫ c(τ , t )u (t − τ f c′t + φ c )
)
+ z (t ) + z (t )
多普勒效应示意图
′ j [ 2 π f c ( t − τ ) + φ c + 2 π f d ( t ) t − 2 π f c′t − φ c ] ′ j [ 2 π (( f c − f c′ ) + f d ( t ))( t − τ ) + ( φ c − φ c )] ′ j [ 2 π (( f c − f c′ + f d ( t )) t − f c τ ) + ( φ c − φ c )]
Auto and Cross Correlation
• Assume φn~U[0,2π] • Recall that θn is the multipath arrival angle • Autocorrelation of inphase/quad signal is
ArI (τ ) = ArQ (τ ) = PEθ n [cos 2πf Dnτ ], f Dn = v cos θ n / λ
• No signal distortion (spreading in time) • Multipath affects complex scale factor in brackets. • Characterize scale factor by setting u(t)=ejφ0
In-Phase and Quadrature under CLT Approximation
• For N(t) large, rI(t) and rQ(t) jointly Gaussian by CLT (sum of large # of random vars). • Received signal characterized by its mean, autocorrelation, and cross correlation. • If ϕn(t) uniform, the in-phase/quad components are mean zero, indep., and stationary.
• 多径信道的冲激响应 模型：
移动信道可以看成线性时 变信道，输入x(t)和输出y(t) 存在以下关系
y (t ) = x(t ) ⊗ h(t , τ )
无线传播信道的模型
s(t)
h(τ, t)
Σ
n(t)
r(t)
• 信道响应为h(τ, t) ，可以表示色散和时变 • 假设：线性信道、加性干扰
Statistical Multipath Model
⎧ r r2 ⎪ exp(− ), p ( r ) = ⎨σ 2 2σ 2 ⎪ 0, ⎩ 0≤r ≤∞ r≤0
• 射频信号受到多普勒衰 落影响的功率谱密度如 右图所示。
Signal Envelope Distribution
• CLT approx. leads to Rayleigh distribution (power is exponential) • When LOS component present, Ricean distribution is used • Measurements support Nakagami distribution in some environments
j ( 2πfct +φc )
s (t )
r (t )
e
′ − j ( 2πf c′t +φc )
v(t )
s ( t ) = Re u ( t ) e v (t ) = u (t − τ )e = u (t − τ )e = u (t − τ )e
)
r ( t ) = s ′ ( t − τ ) + n ( t ) = Re v ( t ) e
Uniform AOAs
• Under uniform scattering, in phase and quad comps have no cross correlation and autocorrelation is
ArI (τ ) = ArQ (τ ) = PJ 0 (2πf Dτ )
Decorrelates over roughly half a wavelength • The PSD of received signal is
– Similar to Ricean, but models “worse than Rayleigh” – Lends itself better to closed-form BER expressions