The Impact of a Wideband Channel on UWB System Design

Transcription

1 EE209AS Spring 2011 Prof. Danijela Cabric Paper Presentation Presented by: Sina Basir-Kazeruni The Impact of a Wideband Channel on UWB System Design by Mike S. W. Chen and Robert W. Brodersen

2 Introduction Communication system design is strongly tied to the characteristics of the wireless channel. In narrowband: Signal bandwidth << Carrier Frequency Central limit theorem can be applied to channel modeling (ex. use of Raleigh and Rician distributions for modeling) As signal bandwidth scales up, assumptions made for narrowband begin to break down. 2

3 UWB Channel Modeling Relationship between transmitted φ(t) and received waveforms y t : L y t = a i (f, t)φ(t τ i (f, t)) i=1 a i (f, t) and τ i (f, t) are the channel gain and arrival time of i t multipath respectively. Assuming system is bandlimited to W, relationship can be expressed in discrete-time version using sampling theory: y[m] = m k= h k, m x[m k] L h k, m = a i f, m W ej2πf cτ i f, m W sinc k Wτi f, m i=1 W 3

4 UWB Channel Modeling Frequency Dependency: In UWB frequency dependency on gain and delay cannot be ignored because of wide signal bandwidth. Received signal waveform gets distorted by communication channels. Coherence Time: Doppler spread. Movement of multipaths between discrete channel taps. 4

5 UWB Channel Modeling Statistical Model: 1. Saleh-Valenzuela Model (S-V): Does not assume multipaths arrive on each sampling time. Two Poisson processes are used to describe the channel. Tap magnitude is Rayleigh distributed. 2. Δ-K Model: A path arrives within time duration Δ according to certain probability. The tap magnitude is lognormal distributed. 3. Nakagami Model: Usually used when central limit theorem does not hold. 4. Lognormal Model: Assumes Rayleigh distribution with exponentially decaying power gain. 5

6 Analysis of Coherent Receiver UWB maximum available bandwidth: 7.5GHz How much BW one should use for optimal performance? Wider transmission bandwidth implies more diversity, however, it also results in higher estimation error for a fixed power constraint. A Linear Least Square Error (LLSE) estimator is used for channel estimation in this paper. 6

7 Analysis of Coherent Receiver Channel Estimation: In the case of L resolvable paths, received signal is expressed in vector form: L y = h i u + w i=1 Received Vector, u, is assumed orthogonal over different resolvable path. Assume pulse energy is mostly confined within 1 W period. Before LLSE estimation, the incoming signal is processed by a matched filter in order to project the signal information onto the correct dimension. 7

8 Analysis of Coherent Receiver Channel Estimation (Cont d): By mapping received signal, y, onto signal dimension, u, we get sufficient statistics, r l (t), at path l: r (l) = u(l). y u Averaging r l K times, channel response and the estimation error for tap l can be derived as following: h l = ε. E h l 2 ε. E h l 2 + N o 2K. 1 K K 1 r k l σ 2 e = E h l 2. N o 2K ε. E h 2 l + N o 2K Where ε is the signal energy; and N o is the channel noise density. 8

9 Analysis of Coherent Receiver Rake Combining: Error event: When the receiver detects zero while transmitter sends one, and vice versa. Error probability can be expressed as: L P e = P V0 > V1 = P h[l](w0 W1 h l. ε) > 0 i=1 = P(X > 0) Where V1, V0 (W1, W0) is the detection energy (noise energy) with and without signal existence. 9

10 Simulations of Coherent Receiver BER vs. Bandwidth Scaling Increase in bandwidth results in increased resolvable paths. The more paths in the system the less energy resides in each path (fixed power budget). BER goes up with bandwidth after about 1GHz, where the estimation error overwhelms the diversity gain. BER vs. Collection Time Simulation Results are based on: Received SNR of 10dB K = 10 Assume X is Gaussian distributed Mean access delay = 13ns Max collection time = 50ns 10

11 Impact of Distorted Matched Filter Significant distortion due to the wideband channel since the receiver cannot perfectly match to the incoming signal. Modeling Matched Filter: Received signal, y t, is the combination of channel gain, h, and waveform distortion, δ t, plus white Gaussian noise, n t. y t = h. s t + δ t + n t where n(t)~n(0, N 0 ), and the matched filter response, p t, 2 matches to the original expected waveform, s t, plus white Gaussian noise, w t. p t = s t + w t, where w(t)~n(0, W 0 2 ) 11

12 Impact of Distorted Matched Filter Modeling Matched Filter (Cont d): Output SNR of the matched filter is defined as the mean and variance ratio at the output of the filter. Following expression shows the relationship between output SNR with non-idealities (δ t and w t ), and ideal SNR for a perfect matched filter: 12

13 Impact of Distorted Matched Filter Imperfect matched filter impact on channel estimation: We can incorporate matched filter non-ideality, δ t, into LLSE estimation: y = L h i. (u + δ) + w i=1 As a result of the non-idealities there will be a term added to the estimation error expression: σ e 2 = σ e,org 2 +σ e,extra 2 13

14 Impact of Distorted Matched Filter Imperfect matched filter impact on channel estimation: Extra estimation error due to distorted matched filter gradually dominates the estimation error as averaging increases for more accuracy. If there is any non-ideality in the matched filter, more averaging will cause error accumulation. 14

15 Questions? 15