Principle of Communications, Fall 2017 Lecture 06 Wireless Communication I-Hsiang Wang ihwang@ntu.edu.tw National Taiwan University 2017/12/27
Recap • Lecture 05 explored wideband communications over wires • Point-to-point communication: single Tx/Rx pair • Physical modeling: ‣ Noise modeled as additive white Gaussian noise ‣ Frequency selectivity modeled as convolution with LTI filter • End-to-end equivalent discrete-time complex baseband channel • Techniques developed: ‣ Optimal detection principles at receiver (Lecture 03) ‣ Error-correction coding to achieve reliable communication in the presence of noise (Lecture 04) ‣ Interference mitigation techniques to combat inter-symbol interference (Lecture 05) • Key feature: channel is quite static and stationary over time. 2
Wireless Communication • Wireless is a shared medium, inherently di ff erent from wireline ‣ More than one pairs of Tx/Rx can share the same wireless medium ‣ ⟹ can support more users , but also more interference ‣ Signals: broadcast at Tx, superimposed at Rx ‣ ⟹ more paths from Tx to Rx (variation over frequency) ‣ Mobility of Tx and Rx ‣ ⟹ channel variation over time ‣ Fading : the scale of variation over time and frequency matters • Key challenges: interference and fading • Look at point-to-point communication and focus on fading ‣ Where does fading come from? ‣ How to combat fading? 3
Outline • Modeling of wireless channels ‣ Physical modeling ‣ Time and frequency coherence ‣ Statistical modeling • Fading and diversity ‣ Impact of fading on signal detection ‣ Diversity techniques 4
Part I. Modeling Wireless Channels Physical Models; Equivalent Complex Baseband Discrete-Time Models; Stochastic Models 5
Multi-Path Physical Model Signals are transmitted using EM waves at a certain frequency f c Far-field assumption: speed of light Tx-Rx distance � λ c � c f c Approximate EM signals as rays under the far-field assumption. Each path corresponds to a ray. The input-output model of the wireless channel (neglect noise) X y ( t ) = a i ( t ) x ( t − τ i ( t )) i 6
X y ( t ) = a i ( t ) x ( t − τ i ( t )) i For path i : a i ( t ) : channel gain (attenuation) of path i τ i ( t ) : propagation delay of path i Simplest example: single line-of-sight (LOS) y ( t ) = α r x ( t − r c ) x ( t ) r τ ( t ) = r a ( t ) = α (free space) ; r c 7
X y ( t ) = a i ( t ) x ( t − τ i ( t )) i Example: single LOS with a reflecting wall d r Path 1: a 1 ( t ) = α r ; τ 1 ( t ) = r c Path 2: a 2 ( t ) = − τ 2 ( t ) = 2 d − r 2 d − r ; α c 8
X y ( t ) = a i ( t ) x ( t − τ i ( t )) i Example: single LOS with a reflecting wall and moving Rx d r ( t ) = r 0 + vt v τ 1 ( t ) = r 0 + vt Path 1: a 1 ( t ) = r 0 + vt ; α c τ 2 ( t ) = 2 d − r 0 − vt Path 2: a 2 ( t ) = − 2 d − r 0 − vt ; α c 9
Linear Time Varying Channel Model X y ( t ) = a i ( t ) x ( t − τ i ( t )) h ( τ ; t ) x ( t ) i Impulse response: X h ( τ ; t ) = a i ( t ) δ ( τ − τ i ( t )) i ˘ Frequency response: X a i ( t ) e − j 2 π f τ i ( t ) h ( f ; t ) = i Equivalent baseband model can be derived, similar to the derivation in wireline communication 10
Continuous-Time Baseband Model X a b y b ( t ) = i ( t ) x b ( t − τ i ( t )) x b ( t ) h b ( τ ; t ) i Impulse response: h b ( τ ; t ) = h ( τ ; t ) e − j2 π f c τ a b i ( t ) , a i ( t ) e − j2 π f c τ i ( t ) X a b = i ( t ) δ ( τ − τ i ( t )) i ˘ h b ( f ; t ) = ˘ Frequency response: h ( f + f c ; t ) The gain of each path is rotated with a phase 11
Discrete-Time Baseband Model X v m = h l [ m ] u m − l h l [ m ] u m l Z ∞ Impulse response: h ` [ m ] , h b ( ⌧ ; mT ) g ( ` T − ⌧ ) d ⌧ −∞ X a b = i ( mT ) g ( ` T − ⌧ i ( mT )) i Recall: g ( t ) is the pulse used in pulse shaping examples: sinc pulse, raised cosine pulse, etc. Observation: The ` -th tap h ` [ m ] majorly consists of the aggregation of paths with delay lying inside the “delay bin” ⌧ i ( mT ) ∈ ` T − T 2 , ` T + T ⇥ ⇤ 2 12
τ 1 τ 2 τ 3 τ 4 τ 5 τ 6 τ 7 τ 8 delay 0 3 T T 2 T 13
ℓ = 0 τ 1 τ 2 τ 3 τ 4 τ 5 τ 6 τ 7 τ 8 delay 0 3 T T 2 T 14
ℓ = 1 τ 1 τ 2 τ 3 τ 4 τ 5 τ 6 τ 7 τ 8 delay 0 3 T T 2 T 15
ℓ = 2 τ 1 τ 2 τ 3 τ 4 τ 5 τ 6 τ 7 τ 8 delay 0 3 T T 2 T 16
ℓ = 3 τ 1 τ 2 τ 3 τ 4 τ 5 τ 6 τ 7 τ 8 delay 0 3 T T 2 T 17
Recommend
More recommend
