MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com On the Spectral and Power Requirements for Ultra-Wideband Transmission Hongsan Sheng, Philip Orlik, Alexander M. Haimovich, Leonard J. Cimini, Jr, Jinyun Zhang TR2003-66 December 2003 Abstract UWB systems based on impulse radio have the potential to provide very high data rates over short distances. In this paper, a new pulse shape is presented that satisfies the FCC spectral mask. Using this pulse, the link budget is calculated to quantify the relationship between data rate and distance. It is shown that UWB can be a good candidate for high rate transmission over short ranges, with the capability for reliably transmitting 100 Mbps over distances at about 10 meters. IEEE International Conference on Communications (ICC) This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c Mitsubishi Electric Research Laboratories, Inc., 2003 201 Broadway, Cambridge, Massachusetts 02139 MERLCoverPageSide2 On the Spectral and Power Requirements for Ultra-Wideband Transmission Hongsan Sheng† Philip Orlik‡ Alexander M. Haimovich† Leonard J. Cimini, Jr.u Jinyun Zhang‡ New Jersey Institute of Technology, Newark, NJ 07102, Email: {hs23, haimovic}@njit.edu Mitsubish† Electric Research Laboratories, Murray Hill, NJ 07974, Email: {porlik, jzhang}@merl.com ‡ u University of Delaware, Newark, DE 19716, Email: [email protected] Abstract— UWB systems based on impulse radio have the II. GAUSSIAN PULSE AND SPECTRUM potential to provide very high data rates over short distances. In A Gaussian pulse is one candidate for the monocycle in this paper, a new pulse shape is presented that satisfies the FCC spectral mask. Using this pulse, the link budget is calculated UWB impulse radio systems. If a Gaussian pulse is trans- to quantify the relationship between data rate and distance. mitted, due to the derivative characteristics of the antenna, It is shown that UWB can be a good candidate for high rate the output of the transmitter antenna can be modeled by the transmission over short ranges, with the capability for reliably first derivative of the Gaussian pulse. Therefore, if a general transmitting 100 Mbps over distances at about 10 meters. Gaussian pulse is given by A t2 I. INTRODUCTION x(t)= exp( ), (1) √2πσ −2σ2 Ultra-wideband (UWB) technology has been proposed as an alternative air interface for Wireless Personal Area Networks then the output of the transmitter antenna will be because of its low power spectral density, high data rate, and At t2 x(1)(t)= exp( ), (2) robustness to multipath fading. The Federal Communications −√2πσ3 −2σ2 Commission (FCC) has defined an intentional UWB device as (n) one that has a bandwidth equal to or greater than 20% of the where the superscript denotes the n-th derivative. The pulse center frequency, or that has a bandwidth equal to or greater at the output of the receiver antenna is then given by than 500 MHz. The FCC has also permitted UWB devices to t2 1 t2 x(2)(t)=A( )exp( ). (3) operate using spectrum occupied by existing radio services as √2πσ5 − √2πσ3 −2σ2 long as emission restrictions, in the form of a spectral mask, are met [1]. A UWB transmitted signal, using PAM, with uniformly spaced Impulse radio is one of the popular choices for UWB pulses in time can be represented as transmission because of its ability to resolve multipath, as well ∞ (n) s(t)= akx (t kT), (4) as the relatively low implementation complexity associated − k= with carrierless (baseband) pulses [2]. Impulse radio does not X−∞ use a sinusoidal carrier to shift the signal to a higher frequency, where T is the pulse-spacing interval and the sequence ak but instead communicates with a baseband signal composed represents the information symbol. The PSD of the transmitted{ } of subnanosecond pulses (referred to as monocycles)[3]. signal, P (f), is [6, p. 207] Because of the short duration of the pulses, the spectrum of 2 2 2 σa 2 µa ∞ k k the UWB signal can be several gigahertz wide. Impulse radio P (f)= Xn(f) + Xn( ) δ(f ), (5) T | | T 2 T − T systems employ a pulse train with pulse amplitude modulation k= ¯ ¯ (PAM) or pulse-position modulation (PPM). Previously, UWB X−∞ ¯ ¯ where X (f) is the Fourier transform¯ of the¯ n-th derivative systems using PAM [4] and PPM [5] have been analyzed, n ¯ ¯ of a Gaussian pulse, σ2 and µ are the variance and mean, especially the distance as a function of throughput. However, a a respectively, of the symbol sequence a ,andδ( ) is the the standard monocycles used in [4] and [5] do not satisfy the k Dirac delta function. The second term{ in} (5), composed· of FCC spectral rules. Here, we analyze the transmission range discrete spectral lines, will vanish if the information symbols as a function of data rate using a new pulse shape that meets have zero mean. In what follows, we assume this is true and the FCC regulations. also assume that σ2 =1. Strictly speaking, the duration of the In this paper, we focus on the spectral and power require- a Gaussian pulse and all of its derivatives is infinite. Here, we ments for UWB transmission. In Section II, we compute the define the pulse width, T , as the interval in which 99.99% power spectral density (PSD) of the Gaussian-based monocy- p of the energy of the pulse is contained. Using this definition, cle, which does not satisfy the regulatory rules. A new pulse it can be shown that T 7σ for the first derivative of the that meets the FCC emission key is proposed in Section III. p Gaussian pulse. ≈ This pulse is based on higher-order derivatives of the Gaussian The FCC has issued UWB emission limits in the form of pulse. In Section IV, the transmission range and data rate of a spectral mask for indoor and outdoor systems [1]. In the a UWB system using the proposed pulse is presented. band from 3.1 GHz to 10.6 GHz, UWB can use the FCC L. Cimini did this work at MERL with MERL’s funding. Part 15 rules with a peak value of 41 dBm/MHz. Outside − 0 pulse and, then choose a pulse shape that meets the emission T =0.15 p requirements. -5 FCC Mask A. Spectrum of Pulses Based on Higher-Order Derivatives ) -10 B d Using the general Gaussian pulse in (1), its n-th derivative ( D can be determined recursively from S -15 P d (n) n 1 (n 2) t (n 1) e T =0.40 x (t)= x (t) x (t). (6) z − − − i -20 p 2 2 l − σ − σ a m r T =0.30 The Fourier transform of the n-th order derivative pulse is o -25 p N 2 n (2πfσ) T =0.25 Xn(f)=A(j2πf) exp .(7) -30 p {− 2 } Consider the amplitude spectrum of the n-th derivative -35 0 5 10 15 2 Frequency (GHz) n (2πfσ) Xn(f) = A(2πf) exp . (8) | | {− 2 } Fig. 1. Power spectral density for the first-derivative Gaussian pulse for The frequency at which the maximum value of (8) is attained, various values of the pulse width. The FCC spectral mask for indoor systems the peak emission frequency, fM , can be found by differenti- is shown for comparison. ating (8) and setting it equal to zero. Differentiating (8) gives 2 d Xn(f) n 1 (2πfσ) 2 | | = A(2πf) − 2π exp [n (2πfσ) ]. of this band, the PSD must be decreased. From 0.96 GHz df {− 2 } − to 1.61 GHz, the reduction in admissible transmitted power (9) is necessary to protect GPS transmissions. To protect PCS The peak emission frequency then must satisfy 2πfM σ = √n, transmission for outdoor systems in the band from 1.99 GHz and the maximum value of the amplitude spectrum is to 3.1 GHz, the required backoff is 20 dB, rather than the 10 √n n n Xn(fM ) = A( ) exp( ). (10) dB for indoor systems. | | σ − 2 In Fig. 1, the normalized PSD for the first derivative (n =1) Define the normalized PSD, Pn(f) , as of the Gaussian pulse is plotted for several values of the pulse | | 2 2n 2 width, Tp. The normalization factor is the peak value allowed Xn(f) (2πfσ) exp (2πfσ) Pn(f) , | | 2 = n {− }, (11) by the FCC, -41 dBm/MHz. It is clear that the PSD of the | | Xn(fM ) n exp( n) first derivative pulse does not meet the FCC requirement no | | − which has a peak value of 1 (0 dB). If we consider the n- matter what value of the pulse width is used. Therefore, a new th derivative of the Gaussian pulse as the UWB transmitted pulse shape must be found that satisfies the FCC emission pulse, then the PSD of the transmitted signal is given by requirements. One possibility is to shift the center frequency 2n 2 and adjust the bandwidth so that the requirements are met. This Amax(2πfσ) exp (2πfσ) Pt(f) Amax Pn(f) = {− }, could be done by modulating the monocycle with a sinusoid to | | , | | nn exp( n) shift the center frequency and by varying the values of σ.For − (12) example, for a pulse width Tp =0.3 ns, by shifting the center where Amax is the peak PSD that the FCC will permit.