Multiuser Interference in TH-UWB Roman Merz, Cyril Botteron, - - PowerPoint PPT Presentation

Outline

Multiuser Interference in TH-UWB

Roman Merz, Cyril Botteron, Pierre-Andr´ e Farine

Institute of Microtechnology University of Neuchˆ atel 2000 Neuchˆ atel

Workshop on UWB for Sensor Networks, 2005

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Outline

Outline

1

Introduction Motivations and Goals Description TH-UWB Receiver Architecture

2

Coherent Addition No Timing Error Gaussian Jitter Frequency Offset

3

Multiuser Interference Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

4

Conclusions

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Motivations and Goals Description TH-UWB Receiver Architecture

Motivations and Goals

Motivations A WSN may contain many nodes UWB is an attractive physical layer technology for WSNs Goals Evaluation of the applicability of a code sequence as a spreading code Evaluation during all receiver’s operating modes, including initial synchronization phase

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Motivations and Goals Description TH-UWB Receiver Architecture

Impulse Radio

No modulation, no spreading t Ts = NfTf Symbol composed of Nf frames Each frame contains one pulse Time Hopping Spreading (TH-UWB) t Tf = NcTc Ts = NfTf A frame is formed by Nc chips Pulse position determined by repetitive spreading code with Nf elements.

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Motivations and Goals Description TH-UWB Receiver Architecture

Receiver Architecture

Subseq

• Ts

Ref Pulse t t t Tf Code A subsequence at the expected time of arrival

• f a pulse is acquired

Several subsequences are added to increase SNR Further processing (correlation, demodulation) is not considered The implementation may be in analog or digital domain

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Motivations and Goals Description TH-UWB Receiver Architecture

Receiver Architecture

Subseq

• Ts

Ref Pulse t t t Correlator with seq. of rectangular templates Tf Code A subsequence at the expected time of arrival

• f a pulse is acquired

Several subsequences are added to increase SNR Further processing (correlation, demodulation) is not considered The implementation may be in analog or digital domain

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions No Timing Error Gaussian Jitter Frequency Offset

No Timing Error

× × × × × × × × × × × × × × × × × × ×

20 25 210 215 5 10 15 20 25 30 35 40 45 Number of coherent additions Nf Pulse combining gain GPC (dB) Theoretical

× Measurement

No timing error: linear pulse combining gain GPC = Nf Gaussian jitter: linear pulse combining gain GPC =

• tn
• t2

n + σ2

5 Nf Frequency offset: non-linear pulse combining gain

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions No Timing Error Gaussian Jitter Frequency Offset

Gaussian Jitter

20 25 210 215 5 10 15 20 25 30 35 40 45 Number of coherent additions Nf Pulse combining gain GPC (dB) 0 ps 100 ps 200 ps 500 ps No timing error: linear pulse combining gain GPC = Nf Gaussian jitter: linear pulse combining gain GPC =

• tn
• t2

n + σ2

5 Nf Frequency offset: non-linear pulse combining gain

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions No Timing Error Gaussian Jitter Frequency Offset

Frequency Offset

1 fs 10 fs 100 fs 1 ps 20 25 210 215 5 10 15 20 25 30 35 40 45 Number of coherent additions Nf Pulse combining gain GPC (dB) No timing error: linear pulse combining gain GPC = Nf Gaussian jitter: linear pulse combining gain GPC =

• tn
• t2

n + σ2

5 Nf Frequency offset: non-linear pulse combining gain

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Frame Synchronization

Frame Synchronized and Code Synchronized t Ts w1,k w2,k w3,k w4,k t wk δ User of interest → coherent addition Serves as a reference scenario for the evaluation Frame Synchronized Erroneous code (not user of interest or wrong code phase) Partially coherent addition Frame Non Synchronized Interferer with unrelated timing

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Frame Synchronization

Frame Synchronized and Code Synchronized Coherent Addition of the user

• f interest

Serves as a reference scenario for the evaluation Frame Synchronized t w1,k w2,k w3,k w4,k t wk Erroneous code (not user of interest or wrong code phase) Partially coherent addition Frame Non Synchronized Interferer with unrelated timing

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Frame Synchronization

Frame Synchronized and Code Synchronized Coherent Addition of the user

• f interest

Serves as a reference scenario for the evaluation Frame Synchronized Erroneous code (not user of interest or wrong code phase) Partially coherent addition Frame Non Synchronized t w1,k w2,k w3,k w4,k t wk Interferer with unrelated timing

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Distinction Coefficient

t w1,k w2,k w3,k w4,k t wk W(a) Maximum absolute value User of interest, synchronized Interferers t w1,k w2,k w3,k w4,k t wk W(b,c) Max (all configurations) Erroneous code Interferers

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Distinction Coefficient

t w1,k w2,k w3,k w4,k t wk W(a) D = W(a)/W(b,c) t w1,k w2,k w3,k w4,k t wk W(b,c)

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Distinction Coefficient

t w1,k w2,k w3,k w4,k t wk W(a) W(a) = Nf maxt q(n)(t) t w1,k w2,k w3,k w4,k t wk W(b,c) W(b,c) = Smax maxt q(n)(t) D = W(a)/W(b,c) Instead of correlating signals, counting the number of “hits” Smax. (Valid if duration of the received pulse is shorter than a chip).

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Results

1 2 3 4 5 6 7 8 2 4 8 16 32 64 128 256 Code length Nf D

b c b c b c b c b c b c b c b c

× × × × × × × ×

b b b b b b b b u t u t u t u t u t u t u t b c b c b c b c b c b c b c b c

× × × × × × × ×

b b b b b b b b u t u t u t u t u t u t u t u t

LFSR RAND

u t 4 bits b 3 bits

× 2 bits

b c 1 bit

Fig: D for LFSR and random spreading codes, without MAI, in PC Distinction coefficient depends on the code length Nf and the number of bits to represent one element of the code.

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Distinction Coefficient

t w1,k w2,k w3,k w4,k t wk W(a) Expected value User of interest, synchronized Frame non synchronized interferers t w1,k w2,k w3,k w4,k t wk W(b,c) max over all expected values mth user all users = m

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Results

1 2 3 4 1 2 4 8 16 32 64 Code length Nf D

b b b b b b

× × × × × × ×

b c b c b c b c b c b c b c u t u t u t u t u t u t u t q p q p q p q p q p q p q p l d l d l d l d l d l d l d

b M = 1

× M = 2

b c M = 3 u t M = 5 q p M = 9 l d M = 17

Fig: D for three bits LFSR code, with MAI, in PC. 1 2 3 4 1 2 4 8 16 32 64 Code length Nf D

b b b b b b

× × × × × × ×

b c b c b c b c b c b c b c u t u t u t u t u t u t u t q p q p q p q p q p q p q p l d l d l d l d l d l d l d b M = 1

× M = 2

b c M = 3 u t M = 5 q p M = 9 l d M = 17

Fig: D for a three bits LFSR code, with MAI, in CM3 channel model.

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Distinction Coefficient

t w1,k w2,k w3,k w4,k t wk W(a) Expected value User of interest, synchronized Frame synchronized interferer t w1,k w2,k w3,k w4,k t wk W(b,c) max over all expected values

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions Definitions Single User Frame Non Synchronized Interference Frame Synchronized Interference

Results

1 2 3 4 2 4 8 16 32 64 Code length Nf D

b b b b b b

× × × × × ×

b c b c b c b c b c b c u t u t u t u t u t u t q p q p q p q p q p q p l d l d l d l d l d l d b b b b b b

× × × × × ×

b c b c b c b c b c b c u t u t u t u t u t u t q p q p q p q p q p q p l d l d l d l d l d l d

no sync sync

b M = 1

× M = 2

b c M = 3 u t M = 5 q p M = 9 l d M = 17

Fig: D for three bits LFSR code, with MAI, in PC. 1 2 3 4 2 4 8 16 32 64 Code length Nf D

b b b b b b

× × × × × ×

b c b c b c b c b c b c u t u t u t u t u t u t q p q p q p q p q p q p l d l d l d l d l d l d b b b b b b

× × × × × ×

b c b c b c b c b c b c u t u t u t u t u t u t q p q p q p q p q p q p l d l d l d l d l d l d

no sync sync

b M = 1

× M = 2

b c M = 3 u t M = 5 q p M = 9 l d M = 17

Fig: D for a three bits LFSR code, with MAI, in CM3 channel model.

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Introduction Coherent Addition Multiuser Interference Conclusions

Conclusions

Evaluation of code properties under idealized conditions Numerical results for more realistic conditions User separation vs. code length and the number of bits to represent one element of the code

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Additional Frames Bibliography

Single User?

1

User of interest exclusively

Compare correct code vs. erroneous code phases Classical analysis: autocorrelation of the generated RF signal

2

One user only, but not the user of interest

Compare correct code of user of interest vs. the largest result receiving the wrong signal Classical analysis: crosscorrelation between the correct RF signal and the received RF signal

Is there a way to obtain the results from the spreading code directly instead of the RF signals?

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Additional Frames Bibliography

Pulse Shape

−0.5 0.0 0.5 1.0 −0.5 0.0 0.5 1.0 t (ns) A (V) 2nd derivative Gaussian pulse tn = 200 ps 1 pJ at 50 Ω

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Additional Frames Bibliography

Frequency Offset

Pulse combining gain GPC = 4t2

n

3Nα2 + 2N 3 − 4t2

n

3Nα2

• exp
• −1

4 N2α2 t2

n

• where α is the time offset of the emitter and receiver clock accumulated

during the frame time Tf (in between two consecutive pulses). The maximum of the pulse combining gain depends on tn/α. For a second derivative Gaussian pulse, the maximum gain is GPC, max ≈ 0.9564tn α which is obtained for Nmax ≈ 1.6102tn α additions.

Merz, Botteron, Farine Multiuser Interference in TH-UWB

Additional Frames Bibliography

Bibliography

• T. Erseghe, “Ultra wide band pulse communications,” Ph.D.

dissertation, Universit` a Degli Studi Di Padova, 2001.

• R. Merz, C. Botteron, P.-A. Farine, and J. Farserotu, “Asymptotical

analysis of timing imperfections in uwb receivers,” in 2nd IEEE Int.

• Conf. on Circuits and Systems for Communications, 2004, Moscow.
• R. Merz, C. Botteron, and P.-A. Farine, “Multiuser interference

during synchronization phase in uwb impulse radio,” in Proc. Int.

• Conf. on Ultra-Wideband, 2005.

Merz, Botteron, Farine Multiuser Interference in TH-UWB