Narrowband Interference Suppression in DS-UWBCommunication Systems Using Digital Delay

FilterEhab M. Shaheen

Department of Electronic WarfareMilitary Technical College

Cairo, Egyptefareed2007@yahoo.com

Abstract—This paper investigates spectrum shaping in ultra-wideband (UWB) communication systems in order to introducespectral nulls to mitigate the impact of in-band narrowbandinterference (NBI) signals in the IEEE 802.15.3a UWB channelmodels. It has been seen that due to the restraint on theirtransmission power levels, UWB systems unavoidably sufferfrom the interference caused by the coexisting systems, makingit extremely difficult to maintain adequate signal-to-noise-and-interference ratio (SNIR) levels. To this end, we propose theuse of a “Digital Delay Filter” scheme, which is designedto generate a spectral null at the frequency being used byexisting narrowband devices. Our results show that NBI canbe effectively suppressed with the use of such null steeringscheme, therefore improving the robustness of UWB systemsto NBI. Also, it will be shown that the proposed delay filteroutperforms a perfectly tuned notch filter.

Keywords; Ultra wideband - IEEE 802.15.3a channelmodels - Narrowband interference.

I. INTRODUCTION

UWB has been widely envisioned as an excellent can-didate for high-speed data rate, low cost, and short rangeindoor wireless communication systems [1]. Accordingto the Federal Communications Commission (FCC) rule,UWB should operate at a transmit power of at most-41.3dBm/MHz to avoid the interference with existingnarrow-band communication systems [2]. However due tothis limitation, UWB system may face major performancedegradation due to the presence of high power in-band nar-rowband operating services [3]-[5]. Therefore, it is greatlynecessary to mitigate the impact of such interference in orderto enhance the UWB BER performance.

The issue of NBI mitigation for UWB communicationsystems has been studied extensively in recent years. Ingeneral two main approaches are proposed, NBI cancellation[6] and NBI avoidance [7]. In the NBI cancellation approachsuch as the suppression schemes based on minimum mean-square error Rake combining, which were suggested in [8]and [9]. In these papers, it has been shown that the com-putation complexity of the tap weights would be increasedwith addition of branches within the Rake receiver as itis driven by the decision statistic. While in NBI avoidanceapproach such as the pulse shaping method presented in [10],

where with the use of eigenvalue decomposition, the UWBpulses are designed such that their spectra have a null at theoperating frequency of the interfering device.

In order to contribute in such research, this paper proposesa NBI suppression scheme, where the NBI signal is modeledas the standard IEEE 802.11a wireless local area network(WLAN). This proposed scheme shows the capability tosuppress the impact of NBI signals on impulse radio ultrawide-band (IR-UWB) communication systems.

The paper is organized as follows. The signal modelsfor UWB, NBI and their associated channel models arepresented in section II. Section III drives the power spec-tral density (PSD) of the delayed transmitted UWB signaland elaborates on the digital delay filtering method whichintroduces spectral null at the interferer pre-defined fre-quency. Section IV presents simulations to the performanceof a direct sequence binary phase shift keying (DS-BPSK)UWB using the suggested digital delay filter scheme in thepresence of NBI at the IEEE 802.11a band in the IEEE802.15.3a UWB channel models. These performances arealso compared with those of unmodified UWB system inthe presence of strong NBI signal and with the performanceobtained by using the notch filter based case. Section Vconcludes this paper.

II. SYSTEM MODEL

A. UWB Signal ModelThe DS-BPSK UWB signal can be written as [10]

s(t) =

∞∑j=−∞

Nc−1∑m=0

djcm · p(t−mTc − jTf ) (1)

Where p(t) is the shape of the transmitted pulse, dj, is thetransmitted jth binary data bit composed of equally likelybits, Nc is the number of chips per bit, Tc is the chipduration, cm represents the spreading signature sequence. Tfis the frame duration and the bit duration can be representedas Tb = NcTc.

B. UWB Channel ModelIn 2003, the IEEE 802.15.3a model was developed by a

standardization group for UWB communication systems in

978-1-4577-1379-8/12/$26.00 ©2012 IEEE 585

order to compare standardization proposals for high-data ratewireless personal area networks [11].

The model is a modified version of the Saleh-Valenzuelamulti-path channel model [12], where it had been recognizedthat multi-path components tend to arrive in clusters of rays.This model is defined for different four radio environments(CM1, CM2, CM3, and CM4) [13].

The discrete time impulse response of the UWB channelis given by [14]

hs(t) =L∑`=0

K∑k=0

ak,` · δ(t− T` − τk,`) (2)

where “`” is the cluster index, and “k” is the ray indexwithin a cluster, where the total number of clusters and raysare denoted by L and K respectively. “ak,`” is the multi-pathfading coefficient of the of the kth ray within the `th cluster,δ(.) is the Kronecker Delta, and the arrival time of the `th

cluster is denoted by “T`”, and that of the kth ray withinthe `th cluster is represented by “τk,`”.

C. NBI Signal and Channel Model

Assume that the NBI signal is modeled as the or-thogonal frequency division multiplexing (OFDM) basedIEEE802.11a WLAN. A general OFDM signal transmittedby the interferer can be written as

I(t) = Re

{ ∞∑i=−∞

N∑n=1

ain·x(t−iTs)·exp[j2πfn(t−τ)+θ

]}(3)

where ain are the complex symbols for the nth subcarrier,N is the number of sub-carriers, x(t) is the NBI transmittedpulse shape, and Ts is the OFDM symbol duration.fn = fo + ∆f

(n− 1− N−1

2

)are the subcarrier frequencies

equally spaced by ∆f and centered at fo.Assuming that the NBI signal is asynchronous with re-

spect to the desired signal, we model τ as a random timedelay and θ as a random variable (r.v.) uniformly distributedin [0, 2π).

The channel impulse response for the NBI signal can bewritten as

hi(t) =N−1∑n=0

αInδ(t− τn) (4)

where αIn are the Rayleigh distributed channel gains andτn are their corresponding time delays.

III. DIGITAL DELAY FILTER

A. Idea of the Digital Delay Filter

The idea of the suggested digital delay filter elaboratedfrom the fact that a binary sequence over a data bit durationTb, is composed of Nc spectral components 1/Tb Hz apart,where Nc is the number of chips per bit, of length Tc.

Note that, the first normal null is located at frequencyNc/Tb Hz. To cancel out any of these spectral components,the sequence is shifted by an amount of time determined

by the order of the component to be nulled and added toor subtracted from itself. For example to null out the nth

spectral line; the sequence is either shifted by “NTc/n” orby ”NTc/2n” and subtracted or added to itself respectively.Spectral components harmonically related to the chosen lineto be cancelled are either strengthened or nulled out resultingin the introduction of rather more nulls in the spectrum ofthe sequence than was originally designed.

Figure (1) depicts the schematic block diagram of a DS-BPSK UWB transmitter modified by the delay filter. Thebinary transmitted sequence enters the code repetition coderblock, which is responsible for producing redundancy byrepeating each bit according to the required number of chipstransmitted per bit Nc. The Binary to 1 Converter blockconverts the input binary stream sequence into +1 and -1 series. The transmission coder block is responsible forgenerating a new sequence, by applying the pseudo randomcode “c” to the binary sequence.

Fig. 1. The Block diagram of the DS-BPSK UWB transmission schemeincluding the proposed digital delay filter.

The output sequence will be BPSK modulated and pulseshaped by the transmitter pulse shaping filter, which includesthe delay filter. The signal enters the delay filter, where it’sshifted by an amount of time equals to the inverse of thepre-defined interferer’s frequency.

The delayed DS-BPSK UWB signal can be written as

sd(t) =∞∑

j=−∞

Nc−1∑m=0

djcm · p(t−mTc − jTf − ε) (5)

Where ε is a time delay.

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The transmitted UWB signal can be written as

stx(t) =∞∑

j=−∞

Nc−1∑m=0

djcm · p(t−mTc − jTf )−

∞∑j=−∞

Nc−1∑m=0

djcm · p(t−mTc − jTf − ε) (6)

The UWB pulse is chosen to be the six derivative Gaus-sian pulse, which can be written as [5]

p(t) =

√640

231Nsτp

[1− 12π

(t

τp

)2

+ 16π2

(t

τp

)4

−

64

15π3

(t

τp

)6]

exp

[−2π

(t

τp

)2]

(7)where τp is the pulse shaping factor.

Its Fourier transform, P(f), can be written as [5]

P (f) =8π3

3√

1155Nsτ13/2p f6e−

π2 f

2τ2p (8)

Figure (2) depicts the normalized transmitted UWB pulsegenerated by the digital delay filter. In this example theduration of the pulse is designed as 0.5ns and τp=0.25ns.

Fig. 2. The transmitted DS-BPSK UWB filtered pulse.

In the receiver side (a Rake receiver in our case), the samedelay will be added to the correlation mask signal.

B. Spectrum of the Transmitted Pulse

In order to prove such idea, the PSD of the transmittedUWB pulse will be derived. Firstly, the auto-correlationfunction of sd(t) can be written as Rss(t, t + τ) =

E{sd(t)s

∗d(t+ τ)

}Rss(t, t+ τ) =

∞∑j1=−∞

∞∑j2=−∞

E{dj1d

∗j2

} Nc−1∑m1=0

Nc−1∑m2=0

cm1·

cm2p(t−m1Tc − j1Tf − ε)p(t+ τ −m2Tc − j2Tf − ε)

(9)Let λ =j2 - j1

Rss(t, t+ τ) =∞∑

j1=−∞

∞∑λ=−∞

Rd(λ)

Nc−1∑m1=0

Nc−1∑m2=0

cm1cm2

p(t

−m1Tc − j1Tf − ε)p(t+ τ −m2Tc − j1Tf − λTf − ε)(10)

Since Sd(t) is a zero-mean stochastic process, it is a wide-sense cyclo-stationary stochastic process with period Tf .

The averaged auto-correlation function can be written as

<̄(τ) =1

Tf

∫ Tf

0

Rss(t, t+ τ)dτ

<̄(τ) =1

Tf

∫ Tf

0

Nc−1∑m1=0

Nc−1∑m2=0

cm1cm2

∞∑j1=−∞

∞∑λ=−∞

Rd(λ)

p(t−m1Tc − j1Tf − ε)p(t+ τ −m2Tc−j1Tf − λTf − ε)

(11)The power spectral density of the delayed signal Sd(t)

can be obtained by evaluating the Fourier transform of theaveraged auto-correlation function as

P ds (f) =

∫ ∞−∞<̄(τ) exp

(− j2πfτ

)dτ (12)

P ds (f) =1

Tf

Nc−1∑m1=0

Nc−1∑m2=0

cm1cm2

∫ ∞−∞

e(−j2πfτ)∞∑

λ=−∞

Rd(λ)

∞∑j1=−∞

∫ Tf

0

p(t−m1Tc − j1Tf − ε)p(t+ τ −m2Tc

- j1Tf−λTf−ε)dtdτ (13)

=1

Tf

Nc−1∑m1=0

Nc−1∑m2=0

cm1cm2

∫ ∞−∞

e(−j2πfτ)∞∑

λ=−∞

Rd(λ)

∞∑j1=−∞

∫ (j1+1)Tf

j1Tf

p(t−m1Tc − ε)p(t+ τ −m2Tc

-λTf−ε)dtdτ (14)

=1

Tf

Nc−1∑m1=0

Nc−1∑m2=0

cm1cm2

∫ ∞−∞

e(−j2πfτ)∞∑

λ=−∞

Rd(λ)

∫ −∞−∞

p(t−m1Tc− ε)p(t+ τ −m2Tc−λTf − ε)dtdτ(15)

=1

Tf

Nc−1∑m1=0

Nc−1∑m2=0

cm1cm2

e−j2πf(m1−m2)Tc e−j4πfε

587

∞∑λ=−∞

Rd(λ)e(−j2πfλTf )∫ −∞−∞

p(t−m1Tc − ε)

·e−j2πf(t−m1Tc−ε)dt

∫ −∞−∞

p(t+τ−m2Tc−λTf−ε)

·e−j2πf(t+τ−m2Tc−λTf−ε)dτ (16)

=1

Tf

Nc−1∑m1=0

Nc−1∑m2=0

cm1cm2 e−j2πf(m1−m2)Tc e−j4ε

·∣∣∣P (f)

∣∣∣2 Ps(f) (17)Similarly, the PSD of the UWB signal without delay can

be written as

Ps(f) =1

Tf

Nc−1∑m1=0

Nc−1∑m2=0

cm1cm2 e−j2πf(m1−m2)Tc

·∣∣∣P (f)

∣∣∣2 Ps(f) (18)

Then, the PSD of the transmitted UWB signal,P txs (f) = Ps(f)± P ds (f), can be written as

P txs (f) =1

Tf

Nc−1∑m1=0

Nc−1∑m2=0

cm1cm2 e−j2πf(m1−m2)Tc

∣∣∣P (f)∣∣∣2

·Ps(f)[1−e−j4πfε

](19)

where Ps(f) is a Fourier transform of Rd(λ),∣∣∣P (f)

∣∣∣2 is theenergy spectral density of the six derivative Gaussian pulse,p(t), and when the transmitted symbols are equiprobable andindependent random variables, Ps(f) = Eb.

In the case of subtracted the time shift and by settingf = fi, and ε = 1/fi, then Ptx(f) = 0, which means a nullwill be obtained in the spectrum of the transmitted UWBsignal at the interferer operating frequency fi. While in thecase of added the time shift and by setting f = fi, and“ε = 1/4fi ”, a null will be obtained in the spectrum of thetransmitted UWB signal at the interferer operating frequencyfi.

Figure (3(a)) depicts the PSD of the UWB signal withoutusing the digital delay filter, whereas figure (3(b)) depictsthe PSD of the UWB transmitted signal with the use of thesuggested digital delay filter. It can be seen that a null canbe obtained assuming that the interferer operating frequencyis 5.745GHz.

IV. NUMERICAL AND SIMULATION RESULTS

In this section the performance of the DS-BPSK UWBsystem in the presence of the standard IEEE 802.11a NBIsignal will be investigated. A six derivative Gaussian re-ceived pulse will be used with values: τp = 0.192 ns, Tf =10 ns, and Ns = 1 pulse/bit. The IEEE 802.11a is assumed tobe operated at the upper U-NII band with center frequency= 5.745GHz, and the frequency spacing between the carriers∆f = 0.3125MHz.

Based on the digital delay filter scheme discussed previ-ously, a spectrum with null at the interferer signal operating

(a) PSD without the digital delay filter

(b) PSD with the digital delay filter, fi = 5.745GHz

Figure 3. DS-BPSK UWB PSD without / with the digital delay filter.

frequency will be presented. A comparison between theperformance of the UWB system in the presence of the NBIsignal with and without the use of the suggested delay filterin the IEEE 802.15.3a (CM1, CM2, CM3 and CM4) UWBchannel models will be presented.

Figure (4) depicts such comparison in the CM1 UWBchannel model for different SIRs = -15, -20 and -25dB. Itcan be seen that, SNR degradation is expected to be lessthan 11 dB for SIR = -25dB at BER = 2x10−3 due to thepresence of the IEEE 802.11a NBI signal.

While the impact of the NBI signal can be suppressedwith the use of the suggested delay filter, SNR degradationis expected to be less than 4dB at BER = 1x10−5.

Figure (5) depicts the performance of the DS-UWBsystem in the CM2 UWB channel model. It can be seenthat the performance of the UWB system is deteriorateddue to the presence of the NBI signal. SNR degradationis expected to be less than 13dB at BER = 3x10−3, whereas

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Fig. 4. BER Performance comparison of the DS-BPSK UWB in thepresence of IEEE802.11a NBI in the CM1 channel model without/with thedigital delay filter, fi = 5.745GHz.

the SNR degradation is reduced to be less than 5dB at BER= 1.6x10−5.

Fig. 5. BER Performance comparison of the DS-BPSK UWB in thepresence of IEEE802.11a NBI in the CM2 channel model without/with thedigital delay filter, fi = 5.745GHz.

Figures (6) and (7) depict such comparison in the CM3and CM4 UWB channel models respectively. It can be seenthat the NBI signal can severely degrade the performanceof the UWB system. For SIR = -25dB, SNR degradation isexpected to be less than 13dB at BER = 4x10−2 and 12dBat BER = 5x10−2 for CM3 and CM4 respectively. This SNRdegradation can be reduced to be less than 2dB at BER =3.8x10−5 and 3dB at BER = 4x10−5 for CM3 and CM4UWB channel models respectively.

Finally figure (8) depicts the performance effectivenessof the proposed delay filter by making a comparison withthe performance obtained by using a notch filter at SIR =

Fig. 6. BER Performance comparison of the DS-BPSK UWB in thepresence of IEEE802.11a NBI in the CM3 channel model without/with thedigital delay filter, fi = 5.745GHz.

Fig. 7. BER Performance comparison of the DS-BPSK UWB in thepresence of IEEE802.11a NBI in the CM4 channel model without/with thedigital delay filter, fi = 5.745GHz.

-25dB in the UWB CM3 channel model. The notch filterwas simulated as a resonator with quality factor (Q = 35)The 3 dB bandwidth of the notch filter with the previousquality factors will be 165 MHz for a WLAN NBI signalwith center frequency = 5.745 GHz. It can be seen that thedelay filter outperforms the perfectly tuned notch filter by5dB at BER = 1x10−5.

V. CONCLUSION

In this paper, a digital delay filter has been introducedand investigated. It has been shown that, this delay filteris capable of enhancing the performance of the DS-BPSKUWB system and suppressing the impact of the presenceof strong IEEE 802.11a NBI signal in the IEEE 802.15.3aUWB channel models.

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Fig. 8. BER performance comparison of the Delayed filter with a perfectlytuned Notch filter in the CM3 channel model.

The PSD of the transmitted UWB pulse has been derived;where it has been proven that the delay filter can generatea spectral null at the operating frequency of the NBI signal.Also, a comparison is done with the performance obtainedby using a perfectly tuned notch filter based case, whereit has been shown that the proposed digital delay filteroutperforms the perfectly tuned notch filter.

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