IEEE P Wireless Personal Area Networks. UWB Channel Model for under 1 GHz

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1 Setember, 4 IEEE P85-4/55r Project Title Date Submitted Source Re: Abstract Purose Notice Release IEEE P85 Wireless Personal Area Networks IEEE P85 Working Grou for Wireless Personal Area Networks (WPANs) UWB Channel Model for under GHz [ Setember 4] [rev: 8 October 4] [Kai Siwiak] [TimeDerivative] [Coral Srings, FL] Adjunct to TG4a channel model document Voice: [ ] Fax: [ ] [ ksiwiak@ieeeorg ] This aer resents a channel model for UWB ulse systems oerating at frequencies below GHz The urose of this document is to rovide IEEE P85 with a MHz- GHz channel model for evaluating location aware wireless systems This document has been reared to assist the IEEE P85 It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s) The material in this document is subject to change in form and content after further study The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein The contributor acknowledges and accets that this contribution becomes the roerty of IEEE and may be made ublicly available by P85 Submission Kai Siwiak, TimeDerivative

2 Setember, 4 IEEE P85-4/55r Introduction a-UWB Channel Model for under GHz The MHz to, MHz channel model was designed with simlicity in mind, and with a direct hysical interretation for imulses and imulse doublets There is no channel model in the current literature that alies to imulse doublets which sread energy over a % bandwidth This model comrises two comonents The first comonent is a deterministic line of sight (LOS) in-room comonent that catures the major reflection sources at low frequencies These reflections are the room walls and floor for the LOS case The ceiling is omitted The second comonent is a non-line of sight (N-LOS) comonent which is based on the Jakes [Jakes 974] model with exonential energy density rofile (EDP) with the addition of directly radiated energy The multiath UWB ulses and imulses are exonentially distributed, their arrival interval is randomly distributed in windows of duration T s The delay sread increases with distance, as is observed in exeriment, thus a hysically realistic roagation law naturally evolves from the model For both the LOS and NLOS cases a signal S(t) contains all of the multiath comonents, weighted by the receiver antenna aerture A e, and by the receiver antenna efficiency η ant The formulation of the multiath comonents, along with the time definition of UWB imulses, and the frequency deendent receiver antenna aerture and efficiency uniquely address the needs of a, MHz channel model The method of signal detection, including the receiver filter and multilication by the receiver temlate, and the signal rocessing will determine which and how many and how efficiently the multiath comonents are utilized, and how accurately ranges are determined The model is caable of evaluating UWB imulse radios in () direct free sace roagation in additive white Gaussian noise (AWGN), () LOS conditions with multiath tyical of a room, and (3) a range on N-LOS conditions with and without direct ath contributions The model outut is a signal rofile in time which is the inut to the UWB receiver The full model code, rendered in Mathcad is given in the Aendix The Line of Sight Model LOS attenuation is free sace intergal over PSD for distances: d<(roomx +RoomY ) / m Where RoomX and RoomY are the room dimensions Multiath is derived from a direct ath and 9 rimary reflections of a room model: - 4 rincial reflections from the walls - ground reflection - 4 rincial corner reflections Multile realizations are utilized by randomly selecting a transmit and a receive oint in the room Submission Kai Siwiak, TimeDerivative

3 Setember, 4 IEEE P85-4/55r The selected oints are no closer than d t from any wall The LOS comonent of the channel model comrises 5 geometrical arameter and 3 signal arameters These are: - Room dimensions RoomX and RoomY, - Minimum distance to a wall dt, - Antenna heights h and h - Average wall and floor reflection coefficient Γ m - Radiated ower sectral density EIRPsd(f) - Receiver antenna aerture A e and antenna efficiency η ant (f) To view (4)-(7) (8)-() T () R RoomY RoomX T h () () R h Side view (3) Figure LOS comonents in a room of dimensions RoomX by RoomY The reflection coefficient is derived from [Honch 99] Figure shows the signal aths between a transmit antenna T and a receive antenna R in an LOS condition in the room Total energy is Submission 3 Kai Siwiak, TimeDerivative

4 Setember, 4 IEEE P85-4/55r accounted for in the room The "excess" energy in the room should is balanced by the average wall-transmitted energy The signals aths are: - Direct ath given by Equation (), - Ground (floor) reflection given by (), - Single wall reflections given by (4) through (7), - Double wall reflections (corner bounces) given by (8) through () The derived arameters include: - Multiath signal rofile S(t) - RMS delay sread τ rms, - the mean ray arrival rate T s - excess energy factor in the room is W x The aarent total energy received at R is greater than would be obtained from a single ath free sace transmission from T because the reflections direct additional time disersed signal coies to the receiver It is imortant to note that the wave roagation along each ath is governed by the hysics of an exanding sherical wave, thus the energy in each ath attenuates as the square of distance The case resembles a Ricean distribution comrising significant energy in a direct ath followed by a decaying multiath rofile On the average, in a 37 m by 46 m room, the energy in the multiath comonents is db below the direct ath energy, thus the total available energy is db higher than contained in just the direct ath The statistics of the multiath comonents are nearly, but not quite described by a Rayleigh distribution Energy conservation dictates that the total energy leaving the room should equal the energy transmitted This can be aroximately checked by observing the roduct of the excess energy factor with the average transmission coefficient W x [ Γ m ] which should be aroximately one The modeled case verifies this within aroximately 6 db The LOS model is secified by Equation (6), and suorted by Equations (3), (4), and (5) in the Aendix Non-Line of Sight Multiath Model: The non line of sight ath is assumed to be described by a modified Ricean EDP As such a total of 3 Ricean arameters lus an additional distance arameter totally secify the multiath rofile The multiath increases with distance, see [Siwiak 3] and [Cassiolli ], and here is modeled by square root of distance d/d t scaled by the constant τ Energy disersed into and increasingly longer multiath rofile naturally results in an increase in the ower law of roagation attenuation Thus the increase by the square root of distance results in an overall inverse 5 ower of distance for multiath comonents Rather than a non-hysical hase Submission 4 Kai Siwiak, TimeDerivative

5 Setember, 4 IEEE P85-4/55r arameter, a random distance variation within the mean interval T m is used to define the time that multiath comonents arrive at the receiver Total energy roagations as an exanding sherical wave, so the basic roagation is inverse square law The unit energy is allocated a fraction K F for the direct comonent, if any, and (-K F ) for the multiath energy The following arameters secific the UWB radio erformance in a N-LOS condition: - RMS delay sread arameter τ s, and initial distance D t - Mean interval between rays T m s - Fraction of energy in direct comonent K F - Radiated ower sectral density EIRPsd(f) - Receiver antenna aerture A e and antenna efficiency η ant (f) The channel model signal rofile is - Multiath signal amlitude rofile S N (t) The recommended arameters are τ =55 ns, and D t = m to aroximately match the NLOS arameters of CM, CM3, and CM4 in [IEEE8 /49] at the required distances, see slide 34 of [IEEE8 4/54] Direct ath energy fraction K F is a arameter that takes on values between for a fully diffuse multiath and for a ure line of sight free sace ath K F is related to the usual Ricean K-factor by K F =K/(+K) or equivalently K=K F /(-K F ), where K F is in the range [, ] and corresondingly K F takes on the range [, ] Recommended values of K F are (a fully diffused multiath, 3 (half the reflected energy fraction in the LOS case), and 6 K F = should be used to establish the radio erformance in AWGN For both channel model comonents, the signal S N (t) contains all of the multiath comonents, weighted by the receiver antenna aerture, and by the receiver antenna efficiency The method of signal detection, signal convolution the receiver filter, multilication by the receiver temlate, and the signal rocessing will determine which and how many and how efficiently the multiath comonents are utilized The N-LOS model is secified by Equation (36), and suorted by Equations (3), (4), (35) and (37) in the Aendix Submission 5 Kai Siwiak, TimeDerivative

6 Setember, 4 IEEE P85-4/55r References [Honch 99] [Jakes 974] [Cassiolli ] [Siwiak 3] W Honcherenko, H L Bertoni, "Mechanisms governing UHF roagation on single floors in modern office buildings," IEEE Transactions on Vehicular Technology, Vol 4, No 4, November 99, W C Jakes Microwave Mobile Communications, American Telehone and Telegrah Co, 974, rerinted: IEEE Press, Piscataway, NJ, 993 D Cassioli, Moe Z Win and Andreas F Molisch, The Ultra-Wide Bandwidth Indoor Channel: from Statistical Model to Simulations, IEEE Journal on Selected Areas on Commun, Vol, 47-57, August K Siwiak, H Bertoni, and S Yano, On the relation between multiath and wave roagation attenuation, Electronic Letters, 9th January 3, Volume 39 Number, 4-43 [IEEE8 /49] Channel Modeling Sub-committee Reort Final, IEEE P85 Working Grou for Wireless Personal Area Networks (WPANs), IEEE document P85-/49r-SG3a, Dec, (Online): htt://grouerieeeorg/grous/8/5/ub//nov/ [IEEE8 4/54] IEEE P85 Working Grou for Wireless Personal Area Networks (WPANs), IEEE document P85-4/54r-TG3a, Set, 4, a-ds-uwb-no-resonse-eq-sot Submission 6 Kai Siwiak, TimeDerivative

7 Setember, 4 IEEE P85-4/55r APPENDIX Mathcad code for the, MHz Channel model Comonents Submission A - Kai Siwiak, TimeDerivative

8 Setember, 4 IEEE 85-4/ 55r UWB Channel Model Comonents for use below GHz - Kai Siwiak Preliminary Draft: Setember 4, rev October 4, rev 8 October 3 The MHz channel model comrises two comonents The first is a LOS in-room comonent that catures the major reflection sources at low frequencies, which are the walls and floor for the LOS case The second is a N-LOS comonent which is based on the Jakes [Jakes 974] model with exonential energy density rofile (EDP) The multiath UWB ulses and imulses are exonentially distributed, their arrival interval is randomly distributed in windows of duration Ts For both cases a signal S(t) contains all of the multiath comonents, weighted by the receiver antenna aerture, and by the receiver antenna efficiency The method of signal detection, signal convolution the receiver filter, multilication by the receiver temlate, and the signal rocessing will determine which and how many and how efficiently the multiath comonents are utilized The LOS Model LOS: attenuation is free sace intergal over PSD: d<(roomx +RoomY ) / m - Direct lus with Γ ower additional single reflection multiaths; Γ 4 from corner reflections - Multiath is derived from 9 rimary reflections of a room model: 4 rincial reflections from the walls ground reflection 4 rincial corner reflections - Multile realizations are utilized The following arameters secific the UWB radio erformance in a room-los condition: () Room dimensions RoomX and RoomY, and minimum distance to a wall dt () Antenna heights h and h () Radiated ower sectral density EIRPsd(f) (3) Receiver antenna aerture Ae (4) Multiath signal rofile S(t) (5) Average reflection coefficient Γm Derived arameters include: - RMS delay sread τrms, - the mean ray arrival rate Ts - excess energy factor in the room is Wx Total energy is accounted for in the room The "excess" energy in the room should be balanced by the average wall-transmitted energy Submission A- of K Siwiak, TimeDerivative

9 Setember, 4 IEEE 85-4/ 55r The geometry for the LOS in-room model is shown in Figure To view (4)-(7) (8)-() T () R RoomY RoomX T h () () R h Side view (3) Figure To and side views of signal aths inside a room Reflections are shown for only one wall and for one corner All four wall and corners are considered in the model Non-Line of Sight Multiath Model The Jakes [Jakes 974] model with exonential EDP will be alied, here for UWB ulses in non-line of sight (NLOS) cases Thus the multiath imulses are exonentially distributed, their arrival interval is randomly distributed in windows of duration Ts The delay sread arameter is a function of distance, [Siwiak 3] and [Cassiolli ], and here is modeled by the square root of distance, see slide 34 of [IEEE8 4/54] This naturally results in a 5 ower law in roagation as a function of distance Submission A- of K Siwiak, TimeDerivative

10 Setember, 4 IEEE 85-4/ 55r The following arameters secific the UWB radio erformance in a N-LOS condition: () RMS delay sread arameter τ s and distance Dt () Mean interval between rays Tm s (3) Fraction of energy in direct ray Kf (4) Radiated ower sectral density EIRPsd(f) (5) Receiver antenna aerture Ae (6) Multiath signal rofile SN(t) For both channel model comonents, the signal SN(t) contains all of the multiath comonents, weighted by the receiver antenna aerture, and by the receiver antenna efficiency The method of signal detection, signal convolution the receiver filter, multilication by the receiver temlate, and the signal rocessing will determine which and how many and how efficiently the multiath comonents are utilized References: [Honch 99] W Honcherenko, H L Bertoni, "Mechanisms governing UHF roagation on single floors in modern office buildings," IEEE Transactions on Vehicular Technology, Vol 4, No 4, November 99, [Jakes 974] W C Jakes Microwave Mobile Communications, American Telehone and Telegrah Co, 974, rerinted: IEEE Press, Piscataway, NJ, 993 [Cassiolli ] D Cassioli, Moe Z Win and Andreas F Molisch, The Ultra-Wide Bandwidth Indoor Channel: from Statistical Model to Simulations, IEEE Journal on Selected Areas on Commun, Vol, 47-57, August [Siwiak 3] K Siwiak, H Bertoni, and S Yano, On the relation between multiath and wave roagation attenuation, Electronic Letters, 9th January 3, Volume 39 Number, 4-43 [IEEE8 /49] Channel Modeling Sub-committee Reort Final, IEEE P85 Working Grou for Wireless Personal Area Networks (WPANs), IEEE document P85-/49r-SG3a, Dec, (Online): htt://grouerieeeorg/grous/8/5/ub//nov/ [IEEE8 4/54] IEEE P85 Working Grou for Wireless Personal Area Networks (WPANs), IEEE document P85-4/54r-TG3a, Set, 4, a-ds-uwb-no-resonse-eq-sot Submission A-3 of K Siwiak, TimeDerivative

11 Setember, 4 IEEE 85-4/ 55r Constants: seed of roagation, m/s c := µ := 4 π MHz := 6 nanosec := 9 Room dimensions for LOS case, m RoomX := 37 RoomY := 46 Minimum distance from walls, m dt := Antenna heights above the floor, m h := h := A room in an office or industrial area is modeled as 4 walls with dimensions RoomX and RoomY (m) The radio devices are at heights h and h, and are at least distance dt from any wall The reflection coefficient Γ is a single average value derived from [Honch 99] A direct ath and ground reflected ath between two radios in the same room is first selected randomly Then the four rincile wall reflections are considered The direct and ground reflected ath are found from: d( x, x, y, y) := ( x x) + ( y y) + ( h h) () gnd( x, x, y, y) := ( x x) + ( y y) + ( h + h) () Searation distance rojected on the ground is dg( x, x, y, y) := ( x x) + ( y y) The rincial reflected aths are the secular images of the direct ath r( x, x, y, y) := ( x x) + ( y + y) + ( h h) (3) (4) r( x, x, y, y) := ( x x) + ( RoomY y y) + ( h h) (5) r3( x, x, y, y) := ( x + x) + ( y y) + ( h h) (6) r4( x, x, y, y) := ( RoomX x x) + ( y y) + ( h h) (7) Corner bank reflection aths - two wall reflections - there are two ossibilities for rojecting each corner image, but both result in the same ath distance: c( x, x, y, y) := ( x + x) + ( y + y) + ( h h) (8) c( x, x, y, y) := ( x + x RoomX) + ( y + y) + ( h h) (9) c3( x, x, y, y) := ( x + x RoomX) + ( y + y RoomY) + ( h h) () c4( x, x, y, y) := ( x + x) + ( y + y RoomY) + ( h h) () Submission A-4 of K Siwiak, TimeDerivative

12 Setember, 4 IEEE 85-4/ 55r Equations ()-() are exercised to comute a statistically significant number of randomly selected aths in the room, and the secular reflected aths are also comuted Nrnd is the counter limit for index i and is set to several thousands to get statistically valid results Coordinates (XR i, YR i ) and (XR i, YR i ) of the two direct ath endoints are selected Number of trials is: Nrnd := i := Nrnd Xr := rnd( RoomX dt) + dt i Xr := rnd( RoomX dt) + dt i Yr := rnd( RoomY dt) + dt i Yr := rnd( RoomY dt) + dt i () Then the direct distances and ground reflected Gr distances are comuted, and the rincile secular wall reflection distances R i, R i, R3 i, R4 i are comuted Corner reflection C, C, C3, C4 are found The ath lengths in excess of the direct ath are er i, er i, er3 i, and er4 i ; and ec, ec, ec3, ec4 ( ) D := d Xr, Xr, Yr, Yr i i i i i ( ) R := r Xr, Xr, Yr, Yr i i i i i ( ) R := r Xr, Xr, Yr, Yr i i i i i ( ) R3 := r3 Xr, Xr, Yr, Yr i i i i i ( ) R4 := r4 Xr, Xr, Yr, Yr i i i i i ( ) Gr := gnd Xr, Xr, Yr, Yr i i i i i ( ) C := c Xr, Xr, Yr, Yr i i i i i ( ) C := c Xr, Xr, Yr, Yr i i i i i ( ) C3 := c3 Xr, Xr, Yr, Yr i i i i i ( ) C4 := c4 Xr, Xr, Yr, Yr i i i i i Dg := dg Xr, Xr, Yr, Yr i i i i i er := R i i er := R i i er3 := R3 i i er4 := R4 i i eg := Gr i i ec := C i i ec := C i i ec3 := C3 i i ec4 := C4 i i ( ) (3) Submission A-5 of K Siwiak, TimeDerivative

13 Setember, 4 IEEE 85-4/ 55r View a subset of oints: x := 3 RoomX 4 Yr x Yr x RoomY Xr x, Xr x Figure A samling of the total oints (X, Y) and (X, Y) 8 6 Yr x 4 Yr x Yr x RoomY Yr x Xr x, Xr x, RoomX Xr x, Xr x Figure 3 Images in the room walls of the reflection oints C are lower left and C are lower right, C3 are uer right and C4 are uer left Submission A-6 of K Siwiak, TimeDerivative

14 Setember, 4 IEEE 85-4/ 55r 8 R x R x er x, er x Figure 4 Energy delay rofile (EDP) vs excess delay: R, R The excess delays is associated with the Y dimension of the room 8 R3 x R4 x er3 x, er4 x Figure 5 Energy delay rofile vs excess delay, R3, R4 The excess delays are associated with the X dimension of the room Submission A-7 of K Siwiak, TimeDerivative

15 Setember, 4 IEEE 85-4/ 55r Gr x Gr x eg x Figure 6 Energy delay rofile vs excess delay, for the ground reflection Gr C x C x C3 x C4 x ec x, ec x, ec3 x, ec4 x Figure 7 Energy delay rofile vs excess delay, for the corner reflections Submission A-8 of K Siwiak, TimeDerivative

16 Setember, 4 IEEE 85-4/ 55r Reflections from the floor and walls Reflection coefficient from concrete or lasterboard is between 3 for deg, for grazing angle of incidence, see [Honch 99] j := 9 Γ j := Γm := mean( Γ) log( Γm ) Γ j = = 473 j = Γm = 58 Γ i i Figure 8 Reflection coefficient vs incident angle for concrete and laster board walls [Honch 99] (4) Considering transmissions through walls, the incidence angle is aroximately bounded between normal incidence and about 45 deg Normal incidence transmission Average incidence transmission log( 3) = 398 Tm := + Γm log( Tm) = 7535 Secondary reflections involve a transmission and one wall interface followed by a reflection from the back side of the wall followed by the reflection from the front side of the wall The secondary reflection are thus on the average down by: 9 Γ m := 9 j = ( ) Γ j Γ j Γ j + Γ m = 84 log( Γ m ) = 464 db (5) The average secondary reflection is more than db attenuated and will be ignored Submission A-9 of K Siwiak, TimeDerivative

17 Setember, 4 IEEE 85-4/ 55r Three distinct grouings of the EDP (energy delay rofile) are evident in Figures 4-7 These occur because there are three distinct mechanisms in oeration the room is a rectangle so reflections associated with the width and length will cluster differently Also the ground reflection deends only on searation distance and on antenna heights h and h The rms delay sread τrms is the second central moment of the ower delay rofile for each of ath The energies relative to a direct ath are the square of the distance ratio: (D/R) The ground reflected comonent is out of the lane of the other comonents, and its energy is additionally weighted by the the rojection of the vertical field vector on the receive antenna, via the ground reflection hence the ground comonent relative energy is aroximately (/Gr) (D/Gr)4 The delay sread is found from tm := i tm := i + R i + + C i R i R4 i C i er + i ( er i) ec + i R i + ( er4 i) ( ec i) + + C i R i er + i Dg i Gr i C i ( er i) ec + i R3 i Gr i C3 i + 4 ( ec i) er3 + i R3 i ( eg i) + C3 i ( er3 i) ec3 + i R4 i C4 i ( ec3 i) er4 + i ec4 i + C4 i Dg i Gr i 4 ec4 i Gr i ( ) 4 4 eg i (6) (7) W := i + R i C i + + R i C i + + R3 i C3 i + + R4 i C4 i + Dg i Gr i 4 Gr i 4 (8) The "total" energy in the room is Wx times the direct ath energy: Wx := mean( W) + log( Wx) = 4 db τrms i := tm i W i tm i W i trms := mean( τrms) log( Wx ) = 8 db (9) Submission A- of K Siwiak, TimeDerivative

18 Setember, 4 IEEE 85-4/ 55r max( τrms) = 759 Finally the rms delay sread τrms is found min( τrms) = 56 trms = 3 meters trms τrms := c and its value for the selected case is τrms 9 = 44 ns ( ) max τrms Figure 5 shows the EDPs vs excess delays for all three sets of of reflections Note the ground reflections (magenta) follow a narrow range of ossibilities An exonential EDP with delay sread τrms is shown as the black trace, but it does not model the room reflections very well Since the room rimary reflections are entirely deterministic, these will be used as the model The clear areas hugging the abscissa and the ordinate result from setting the two antenna heights to different values c 9 = 5866 scale := ns () uu := 5 R x R x R3 x R4 x Gr x ( f uu ) Dg x Gr x := trms f := ex uu uu scale trms e er x, er x, er3 x, er4 x, eg x, uu scale Figure 9 Energy delay rofile vs excess delay (m) for all wall reflected comonents comared with exonential EDP Submission A- of K Siwiak, TimeDerivative

19 Setember, 4 IEEE 85-4/ 55r The "corner bank shots" trms C x C x C3 x C4 x ( ) f uu e ec x, ec x, ec3 x, ec4 x, uu scale Figure Energy delay rofile vs excess delay (m) for all corner reflected comonents comared with exonential EDP An exonential EDP is not a very good fit to the room calculation Since this case is deterministic, the actual 9-reflection room model can be used Submission A- of K Siwiak, TimeDerivative

20 Setember, 4 IEEE 85-4/ 55r Relative energy = trms R x R x R3 x R4 x Gr x C x C x C3 x C4 x ( ) Γm f uu ( ) Dg x Gr x Γm e Γm 4 e er x, er x, er3 x, er4 x, eg x, ec x, ec x, ec3 x, ec4 x, uu scale meters Figure Multiath Energy vs excess delay, m, for all comonents Solid line reresents an exonential distribution with the same delay sread Submission A-3 of K Siwiak, TimeDerivative

21 Setember, 4 IEEE 85-4/ 55r A mean excess delay is found from Delay := i er i + ec i + er + er3 + er4 + eg i i i i + ec + ec3 + ec4 i i i 9 () Dmn := mean( Delay) Dmn = 878 m median( Delay) = 933 median( Delay) 9 = 978 c nanoseconds The mean ray arrival interval Ts is derived form the mean excess delay Ts := Dmn c Ts 9 = 96 ns () We now have all the required comonents for the multiath ortion of a channel model For the line of sight (LOS) model comonents, we have a direct ath d, and wall reflected multiath comonents that carry energy in addition to the free sace ath between the transmitter and the receiver The i-th realization of the in-room LOS channel imulse resonse field sectral density is thus: H LOSi ( t) := Vfs i ( d) Dg i Γm Gr i Vfs ( d + eg eg + ) δ t c er Γm Vfs i ( d + er) δ t Γm ec + + Vfs c i ( d + ec) δt c er + Vfs i ( d + er) δ t c Vfs i ( d + ec) δ ec t + c er3 + Vfs i ( d + er) δ t ec3 + Vfs i ( d + ec) δ t c c er4 + Vfs i ( d + er) δ t ec4 + Vfs i ( d + ec) δ t c c and the magnetic field strength sectral density at distance d is based on a sherical wave Vfs( d, f) EIRPsd( f) µ c := 4π d (3) (4) where EIRPsd(f) is the effective isotroically radiated ower sectral density at frequency f Submission A-4 of K Siwiak, TimeDerivative

22 Setember, 4 IEEE 85-4/ 55r := m := 9 One, m-th, realization; normalized to direct comonent R m 8 trms Yr m 4 R m 6 Yr m R3 m 4 Xr m, Xr m R4 m Gr m Dg m Gr m C m C m 4 C3 m 6 C4 m er m, er m, er3 m, er4 m, eg m, ec m, ec m, ec3 m, ec4 m Figure One articular realization of the LOS channel imulse amlitude resonse Submission A-5 of K Siwiak, TimeDerivative

23 Setember, 4 IEEE 85-4/ 55r := R m 9 trms Yr m 4 R m 8 Yr m R3 m 7 Xr m, Xr m R4 m 6 Gr m Dg m Gr m 5 C m 4 C m 3 C3 m C4 m er m, er m, er3 m, er4 m, eg m, ec m, ec m, ec3 m, ec4 m Figure 3 One articular realization of the LOS channel imulse energy resonse Submission A-6 of K Siwiak, TimeDerivative

24 Setember, 4 IEEE 85-4/ 55r Plot multile realizations of the model: x := 75 := a := a D := a3 i D := a4 i D := a5 i := i R i R i R3 i R4 i Gr i i i i i a6 D := i a7 Γm D i := a8 Γm D i := a9 := i C i i C i i C3 i i C4 i Dg i Gr i trms 4 a x a x 5 Yr x Yr x a3 x a4 x Xr x, Xr x a5 x a6 x a7 x a8 x 5 a9 x er x, er x, er3 x, er4 x, eg x, ec x, ec x, ec3 x, ec4 x, uu scale Figure 4 Multile realizations of the LOS channel imulse amlitude resonses Submission A-7 of K Siwiak, TimeDerivative

25 Setember, 4 IEEE 85-4/ 55r The receiver antenna aerture is: where: η ant ( f ) 5 4 π f f Ae := f f f f c f f f η ant ( f) EIRPsd( f) df EIRPsd( f ) df is the antenna efficiency as a function of frequency (5) EIRPsd( f) is the radiated effective istroically radiated ower sectral density Thus the collected signal at the receiver is: S( t) := H LOSi ( t) Ae (6) Signal S(t) contains all of the multiath comonents, weighted by the receiver antenna aerture, and by the receiver antenna efficiency The method of signal detection, signal convolution the receiver filter, multilication by the receiver temlate, and the signal rocessing will determine which and how many and how efficiently the multiath comonents are utilized The following arameters secific the UWB radio erformance in a room-los condition: () Room dimensions RoomX and RoomY, and minimum distance to a wall dt () Antenna heights h and h () Radiated ower sectral density EIRPsd(f) (3) Receiver antenna aerture Ae (4) Multiath signal rofile S(t) (5) Average reflection coefficient Γm Derived arameters include: - RMS delay sread τrms, - the mean ray arrival rate Ts - excess energy factor in the room is Wx Here: RoomX = 37 RoomY = 46 h = h = m m m m τrms = 44 9 Ts = 96 9 Wx = 6 Accounting for the total energy, the "excess" energy in the room Wx should aroximately be balanced by the average wall-transmitted energy, thus: log[(wx)( - Γm )] should aroximately equal db and sec sec ( ) Wx log Γm = 6 db (7) Submission A-8 of K Siwiak, TimeDerivative

26 Setember, 4 IEEE 85-4/ 55r Non-Line of Sight Multiath Model The Jakes [Jakes 974] model with exonential EDP will be alied, here for UWB ulses in non-line of sight (NLOS) cases Thus the multiath imulses are exonentially distributed, their arrival interval is randomly distributed in windows of duration Ts Jakes Channel Model for f < MHz follows To test the equations, let the initial delay sread equal τrms where τrms := nanosec The mean ray Tm arrival interval is based on the LOS room model A total of nine aths with a mean delay of Ts were found Thus the mean ray arrival interval is Ts/9: Tm Ts 9 := Tm = 33 (8) 9 For now, we let Ts be artificially small by a factor of R, equivalent to R realizations of the channel model R := The maximum number of comonents considers is Kmax := ceil τrms R Kmax = 938 k := Kmax Tm The multiath comonents are randomly distributed in "bins" that are Ts wide and saced Ts T := Tm k R ( k + rnd( ) ) T = 5 (9) Channel coefficient h is normally distributed with unity standard deviation: hk := rnorm( Kmax +,, ) (3) (sanity check): mean( hk) = 35 stdev( hk) = 6 Tm σa := ex σa = (3) τrms R T k σ k := σa ex σ = τrms (3) Check the result ( σ k ) ( ) Kmax σ k := mean σ = 993 ( ) (33) h := σ k k hk h := h mean( h) Kmax = (34) k k k Submission A-9 of K Siwiak, TimeDerivative

27 Setember, 4 IEEE 85-4/ 55r Hdelay := σa e Hdelay = 6 τrms := nanosec tau := τrms nanosec tu := Square root of ower delay rofile z := τrms nanosec 5 τrms nanosec z h k σa ex tu z tau 5 5 tu z σa ex tau Hdelay Figure 5 T k nanosec, tu, tu Multile realizations of the NLOS channel model at a fixed distance NLOS multiath model: Kmax = 938 ( ) H NLOS ( t) := Vfs( d) Kf δ( ) + Kf Kmax h δ t Ts k ( k ) Vfs d + c Ts k k = Ts k ( ) δ t c (35) The receiver antenna aerture Ae is given by equation (5) Thus the collected signal at the receiver is: S N ( t) := HN LOSi ( t) Ae (36) Submission A- of K Siwiak, TimeDerivative

28 Setember, 4 IEEE 85-4/ 55r The delay sread arameter is a function of distance, [Siwiak 3] and [Cassiolli ], and here is modeled by the square root of distance, see slide 34 of [IEEE8 4/54] Thus ( ) := τ τrmsn d, Dt, τ d Dt A value for τ and Dt that aroximately match channel models CM, CM3, and CM4 in their aroriate distances [IEEE8 /49] is: (37) τ := 55 Dt := (38) Thus ( ) = 7778 τrmsn, Dt, τ ( ) = 455 τrmsn 7, Dt, τ ( ) = 4597 τrmsn, Dt, τ ( ) = 3889 τrmsn 5, Dt, τ ( ) = 55 τrmsn, Dt, τ The choice of trms increasing as the squareroot of distance will result in an average ower law behavior of aroximately 5 for a receiver not emloying a rake or channel equalization technique Signal SN(t) contains all of the multiath comonents, weighted by the receiver antenna aerture, and by the receiver antenna efficiency The method of signal detection, signal convolution the receiver filter, multilication by the receiver temlate, and the signal rocessing will determine which and how many and how efficiently the multiath comonents are utilized The following arameters secific the UWB radio erformance in a N-LOS condition: () RMS delay sread arameter τ s mulitlied by the square root of d/dt () Mean interval between rays Tm s (3) Fraction of energy in direct ray Kf (4) Radiated ower sectral density EIRPsd(f) (5) Receiver antenna aerture Ae (6) Multiath signal rofile SN(t) The Ricean K factor and Kf are related by: Kf=K/(K+), or equaivalently K=Kf/(-Kf), where Kf takes on the range [, ] and corresondingly, Kf takes on the range [, ] Here: τ = 55 nanosec Tm = 33 nanosec nanosec Submission A- of K Siwiak, TimeDerivative