MEASUREMENT AND MODELING OF INDOOR UWB CHANNEL AT 5 GHz

Transcription

1 MEASUREMENT AND MODELING OF INDOOR UWB CHANNEL AT 5 GHz Rutgers University July 31, 2002 Saeed S. Ghassemzadeh saeedg@research.att.com Florham Park, New Jersey This work is based on collaborations between the author and many present and former colleagues at both AT&T and Rutgers WINLAB. Special recognition and thanks go to: Larry J. Greenstein (WINLAB); Vahid Tarokh and Thorvardur Sveinsson (Harvard University); Rittwik Jana, Robert Miller, Christopher W. Rice, William Turin (AT&T); and Vinko Erceg (Zyray Wireless).

2 Outline Motivation Measurement technique and database Path Loss (PL): Data reduction and key findings Model and simulation Multipath Intensity Profile (MIP): Data reduction and key findings on time domain parameters Average relative MIP and its variations Model and simulation Conclusion Future work WINLAB-2

3 In-Home Broadband Wireless Distribution Entertainment Distribution Broadband Services Cable XDSL Fixed Wireless Ultra-Wideband Gateway Telephone / Fax Distribution Wireless Data Network WINLAB-3

4 Motivation To create a channel model for UWB channel that: Represents a realistic UWB channel without doing a costly sounding experiments. Signifies a compact and simple method to simulate the multipath channel behavior. Is useable for range and performance evaluation of various PHYs in-home environment. Most wireless channel models available, either: Do not represent UWB channel, Or are not in the environment and/or frequency spectrum of interest, Or have database that is small for statistical characterization of the channel parameters. WINLAB-4

5 Swept Frequency Measurement Technique Center frequency: 5 GHz fi Df = MHz, t Frequency bins: 401 max = ns Bandwidth: 1.25 GHz fi Dt = 0.8 ns Sweep rate: 400 ms Complex Frequency Response of UWB Channel Complex Impulse Response of UWB Channel IDFT [1] S.J. Howard, K. Pahlavan, Measurement and Analysis of the indoor radio channel in the frequency domain, IEEE Trans. Instrum. Measure., 39: , Oct WINLAB-5

6 Channel Sounder System Block Diagram LABTOP SOFTWARE HP-VEE Programs VNA / PC Controller HP-VEE Programs Data Collection MATLAB Programs Post-Processing HPIB I/O Vector Network Analyzer B RF Out P A D BPF Rx21 LNA PA P A D L = db 150 cable Tx Antenna BPF Rx11 LNA P A D Antenna 1 Agilent 8753-ES A BPF Rx22 LNA P A D L = db 150 cable BPF Rx12 LNA P A D Antenna 2 WINLAB-6

7 Indoor UWB Channel Sounder WINLAB-7

8 Data Base Data base Includes: Measurements at 5 GHz and 1.25 GHz ultra-wideband channel T-R separations ranging from 1m to ~15 m Simultaneous measurements of 2 antennas separated by 38 inches at each location over 2 minute intervals From one wall to maximum of 4 walls penetration 300,000 complex frequency responses at 712 locations in 23 different homes WINLAB-8

9 Measurement Set-up Transmit and receive antennas were separated such that T-R separations have uniform distribution. Measurements were performed in Line-of-Sight (LOS) and None Line-of- Sight (NLS). T-R separations in 1m to 15m in steps of ~ 0.9 m. WINLAB-9

10 Path Loss (PL): Data Reduction We define path loss as: GGP r t t Pr Pl( d ) = ; where Pr Pt 1 = H( fi, tj; d) MN i= 1 i= 1 Typical representation of path loss vs. distance (d): d o is a reference distance, e.g., d o = 1 m. Bracketed term is a least-squares fit to pathloss, PL(d). PL 0 ( intercept) and γ (path loss exponent) are chosen to 2 minimize S. S is the random scatter about the regression line, assumed to be a zero-mean Gaussian variate with standard deviation σ db. N M ( d ) d PL( d) = PL + 10γ log + S; d d = Average received power = Transmit power 2 WINLAB-10

11 Path Loss vs. Distance Scatter Plot A fix path loss model over the population of data does not reproduce the variation due to individual homes. Intercept point, PL o, is 47 db and 50.5 db in LOS and NLOS. Path loss exponent, γ, is 1.7 and 3.1 for LOS and NLOS. WINLAB-11

12 CDF of Shadow fading Shadow-fading is log-normal as expected with zero mean and variance (over the population of data) of about 2.8 and 4.4 db, in LOS and NLOS, respectively. WINLAB-12

13 Path Loss: Key Findings The intercept point depends on the materials blocking the signal within 1m of T-R separation and the home structure. The measured values of PL o for NLS were very close to that of LOS path loss plus a few db more loss due to the obstacle(s) blocking the LOS path. We chose the intercept value to be the mean measured path loss at 1m in 23 homes. Path loss exponent, γ, changes from one home to another. It is a Normal RV with N LOS [1.7, 0.3] and N NLOS [3.5, 0.97]. Shadow-fading, S, is zero mean Gaussian RV with variance that also changes from one home to another. This variance is also a Normal RV with N LOS [1.6, 0.5] and N NLOS [2.7, 0.98]. [2] V. Erceg, et.al., "An empirically based path loss model for wireless channels in suburban environments", IEEE JSAC, vol. 17, no. 7, pp , July WINLAB-13

14 CDF of Path Loss Exponents Path loss exponent is a Normal random variable with N LOS [1.7, 0.3] and N NLOS [3.5, 0.97]. WINLAB-14

15 CDF of Variance of Shadow Fading Variance of shadow fading is a Normal random variable with N LOS [1.6, 0.5] and N NLOS [2.7, 0.98]. WINLAB-15

16 The Path Loss Model Introducing three new RVs: γ = µ + nσ S= nσ, and σ = µ + nσ PL( d) = PL + 10γ log d + S db 0 10 γ 1 γ, 2 σ 3 ( µ γ 1σ γ ) 10 2 ( µ σ 3σσ ) PLo 10 n log d n n PL o 10µ log1 0 d + γ + 10n1σ γ log10d n2µ σ + n2n 3σ σ = = + = Median path loss + Random variation about median path loss σ ; d d 15 m n 1, n 2 and n 3 are iid zero-mean, unit-variance Gaussian variates. n 1 varies from one home to another while n 2 and n 3 vary from one location to another within each home. The variable part of above equation is not exactly Gaussian since n 2 n 3 is not Gaussian. However, this product is small w.r.t. the other two Gaussian terms. Therefore, it can be approximated as a zero mean random variate with standard deviation of: o ( d ) 2 σ = 100σ log + µ + σ var γ 10 σ σ WINLAB-16

17 Model Simulation For simulation purposes, it is practical to use truncated Gaussian distributions for n 1, n 2, n 3 keeping g, s and S from taking on unrealistic values. One possible range for these values are: n [ 0.75,0.75] 1 n, n [ 2,2] 2 3 WINLAB-17

18 UWB Path Loss Model PL ( d ) = PLo + 10µ log d + 10nσ log d+ n µ nnσ ; do d 15 m db = Median path loss γ 10 1 γ 10 2 σ σ + Random variation about median path loss n [ 0.75,0.75] 1 n, n [ 2,2] 2 3 WINLAB-18

19 MIP: Data Reduction The following steps are taken to get the MIPs : Calibration information is removed from the raw data. The response is then locally averaged over time (since the receiver was kept stationary and maximum Doppler measured was no more than a few tenths of Hz.). 401 point complex IFFT is taken to get the complex MIPs. The MIPs are then normalized to the total average power. Threshold (-30 db) is set to +10 db above the average noise floor (-40 db). The noise is removed from the data and MIP is re-normalized so that the area under MIP is one. All MIPs are synchronized w.r.t. their delay at zero ns, representing the first return above the threshold. WINLAB-19

20 RMS Delay Spread and Coherence Bandwidth The rms delay spread is defined as: Hh τrms i= 1 2 τ τ 2 where τ Frequency Correlation Function: Note : R n L i = 1 L τ h(, t) n i i = 1 τ τ i h(, t) 1 N k (,0) = *(, ) (, ), 0 Hh N k i i k i = 1 N 2 R k H f t H f t k (0,0) = 1 H( f, t) PG= N k i Mean Path Gain Defining as 3-dB width of R ( kt, ) and using inverse relationship between B c Hh B c and τ rms, then: B τ α c = K S RMS Bc = 10 log B = 10 log K 10 α log τ + 10 log S 3dB 10 c rms 10 i 2 2 WINLAB-20

21 Time/Frequency Domain Channel Parameters Excess delay and rms delay spread: Maximum excess delay observed was 70 ns. rms delay spread has a normal distribution over all locations and homes. RMS delay spread increases with T-R separation and therefore with path loss. Min. and Max. of rms delay spread: LOS: 1.1ns and 16.6 ns NLS: 0.75 ns and 21 ns Mean and Standard deviation of RMS delay spread: LOS: 4.7 and 2.2 ns NLS: 8.4 ns and 3.8 ns WINLAB-21

22 Time/Frequency Domain Channel Parameters Coherence Bandwidth: Average coherence bandwidth is about 90 MHz and 29 MHz in LOS and NLS, respectively. Maximum Doppler frequency observed was 0.1Hz. WINLAB-22

23 Distribution of RMS Delay Spread, t RMS WINLAB-23

24 RMS Delay Spread vs. T-R Separation WINLAB-24

25 RMS Delay Spread vs. Path Loss WINLAB-25

26 UWB Frequency Correlation Function Probability C b less than abscissa LOS Data NLS Data dB width Correlation Functio n (M Hz) Frequency Correlation LOS Data NLS Data Frequency Separation (MHz) WINLAB-26

27 Relationship Between C b and τ rms 1000 NLS Data LS Fit, B c db = log 10 (σ RMS ) 100 B c (MHz) 10 Slope ~ MHz per 10 nsec, σ Bc = 61.49, MHz σ RMS (nsec) WINLAB-27

28 Relationship Between C b and τ rms 1000 LOS Data LS Fit, B c db = log 10 (σ RMS ) 100 B c (MHz) 10 Slope ~ MHz per 10 nsec, σ Bc = 103.8, MHz σ RMS (nsec) WINLAB-28

29 Doppler-Power Spectrum F d = db Bandwidth WINLAB-29

30 The Relative MIP Model Tapped-delay line model with randomly selected relative MIP power, random amplitude and phase variation. Relative MIP Model Z -1 Path 1 P m1 a 1 +jb 1 S P P mi T P = L = i= 1 Path_ Loss P relative_ i P P T relative_ i Path L P ml Z -L a L +jb L WINLAB-30

31 Average Relative MIP Relative MIPs are MIPs that are averaged over all locations in homes prior to normalization to their maximum power. WINLAB-31

32 Multipath Amplitude and Phase Distribution The multipath amplitudes undergo small variation which can be best characterized by Rician distribution with a K-factor greater than 40 db. The phases of the multipath components are uniformly distributed between 0 and 2p (Note: We can assume also same distribution for carrier-less transmissions with equal probability and uniform distribution, phases taking on values of 1 or 1). The decibel-variation of multipath components are correlated with correlation coefficient r: 0 ρ 0.25 WINLAB-32

33 The Relative MIP Model Concept NLS Typical representation of the multipath delay profile shape has been reported as a decaying exponential. Following this intuition and observing the randomness of the shape of profile over the population of our data, we formed the following function: Prel ( τ ) db = ατ + S where a is decibel-decay constant and S is the decibel-variation about the median relative MIP. The model assumes that the power of the first return for median relative MIP is the strongest one. This simplified the model considerably with insignificant increase in the slope. WINLAB-33

34 The Relative MIP Model Concept NLS at term is a least square fit to the decibel-power of each multipath component. a is then found such that the MSE of S is minimized. We then characterize a and S over the population of homes. We observed the following: - Value of a [db/ns] are normally distributed RVs, N[-0.50, 0.13]. - Values of S [db] are normally distributed RVs N[-0.41, 7.80]. - The mean of S was constant in each home; however, we observed that the standard deviation of S, s S, changes from one home to another. This variation was normally distributed over all homes with N[7.20, 0.88]. WINLAB-34

35 The Relative MIP Model NLS WINLAB-35

36 Distribution of S Over All Homes NLS WINLAB-36

37 Distribution of s S Over All Homes NLS WINLAB-37

38 Distribution of a Over All Homes NLS WINLAB-38

39 The Relative MIP Model NLS Introducing 3 RVs: α = µ + nσ S= µ + nσ and σ = µ + nσ P rel () τ db = ατ + S α 1 α, s 2 s s σs 3 σs ( s s) = ( µ α σα) τ µ s ( µ σ σσ ) = ( µ + nσ ) τ + µ + nσ + n + + n + n α 1 α 2 = µτ + µ + n σ τ n µ + n nσ d d 15 m α s 1 α + 2 σ s σs o 2 s 3 = Median delay profile + Random variation about median delay profile n 1, n 2 and n 3 are iid zero-mean, unit-variance Gaussian variates. n 2 is a fast-varying RV and varies from one delay to another. n 1 and n 3 are slow varying RVs and vary from one home to another. The variable part of above equation is not exactly Gaussian since n 2 n 3 is not Gaussian. However, this product is small w.r.t. the other two Gaussian terms. s WINLAB-39

40 Flowchart for the Channel Simulator Start Generate n1, n2 and n3 Generate RVs {a and S and s} from the model equation Generate t i ; i = 0:89 Plug constants into the model equation Normalize to maximum Assign 30 TH (Threshold) 0 db Set i = 0 P(t i ) db TH db Keep the multipath component Record its delay and relative power Drop the multipath component i =i + 1 Done? Complex Channel Impulse response Scale Rician coefficients by this path power and rotate its phase by a uniformly selected phase Sum all paths. Sum the relative power of all multipaths (i.e. Total channel power) Multiply the linear power of each multipath by path loss an divide by total channel power (i.e. multipath component power). WINLAB-40

41 Live Channel Simulation Show WINLAB-41

42 Channel Simulator Results We simulated the model to compare its statistical behavior with that of measured data. Specifically, we looked at: CDF of t RMS : Simulated vs. measured. Average simulated profile vs. measured. Standard deviation of the model variation about the median: Simulated vs. measured. WINLAB-42

43 CDF of t RMS : Simulated vs. Measured WINLAB-43

44 Average MIP: Simulated vs. Measured WINLAB-44

45 Model Error: Simulated vs. Measured WINLAB-45

46 The Relative MIP Model LOS WINLAB-46

47 The Relative MIP Model- LOS Introducing four RVs: α = µ + σ = µ + σ = µ + σ σ = µ + σ α n1 α, C c n2 c, S s n3 s, and s σ n4 σ db ( ) ( s) P () τ = C+ ατ + S u τ 0.8n rel ( ) ( µ c n2σ c) + ( µ α n1σα) τ µ s 3( µ σ 4σσ ) µ c+ τµ α + µ s u( τ 08. ns) nσc + nσατ + n µ σ + n nσσ ) u ( τ 0.8ns) do = n + n u( τ 0.8 ns) = + d 15 m & τ 0 = 2 1 Median delay profile Random variation about median delay profile WINLAB-47

48 Distribution of C and a WINLAB-48

49 Distribution of S and s S WINLAB-49

50 Conclusion We reported on the statistics and dependencies of channel parameters such as path loss, shadowing, delay spread, Doppler spectrum and average MIP for UWB indoor channels. We presented simple statistical model for multipath that is easily integrated with the path loss model. The models are based on over 300,000 UWB frequency responses at 712 locations in 23 homes. The models statistically regenerates the properties of the indoor channel with small error. The model can be used for simulation and performance evaluation of the UWB systems and can be upgraded with further measurements. WINLAB-50

51 Work in Progress UWB Coexistence: Analysis, Simulation and Measurements. UWB Propagation in Commercial Buildings with 4GHz bandwidth. MIMO Measurements (2x2 or 4x4?) WINLAB-51