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Optimal Waveforms Design for Ultra-Wideband Impulse Radio Sensors

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Optimal Waveforms Design for Ultra-Wideband Impulse Radio Sensors Sensors, 2010, 10, 11038-11063; doi:10.3390/s101211038 OPEN ACCESS sensors ISSN 1424-8220 www.mdpi.com/journal/sensors Article Optimal Waveforms Design for Ultra-Wideband Impulse Radio Sensors Bin Li 1,2,*, Zheng Zhou 1,2, Weixia Zou 1,2, Dejian Li 1,2 and Chong Zhao 2 1 Key Lab of Universal Wireless Communications, Ministry of Education (MOE), Inner Box. 96, BUPT, Beijing 100876, China 2 Beijing University of Posts and Telecommunications (BUPT), Inner Box. 96, BUPT, Beijing 100876, China; E-Mails: [email protected] (Z.Z.); [email protected] (W.X.Z.); [email protected] (D.J.L.); [email protected] (C.Z.) * Author to whom correspondence should be addressed: E-Mail: [email protected]; Tel.: +86-010-6228-3093. Received: 20 October 2010; in revised form: 25 November 2010 / Accepted: 27 November 2010 / Published: 6 December 2010 Abstract: Ultra-wideband impulse radio (UWB-IR) sensors should comply entirely with the regulatory spectral limits for elegant coexistence. Under this premise, it is desirable for UWB pulses to improve frequency utilization to guarantee the transmission reliability. Meanwhile, orthogonal waveform division multiple-access (WDMA) is significant to mitigate mutual interferences in UWB sensor networks. Motivated by the considerations, we suggest in this paper a low complexity pulse forming technique, and its efficient implementation on DSP is investigated. The UWB pulse is derived preliminarily with the objective of minimizing the mean square error (MSE) between designed power spectrum density (PSD) and the emission mask. Subsequently, this pulse is iteratively modified until its PSD completely conforms to spectral constraints. The orthogonal restriction is then analyzed and different algorithms have been presented. Simulation demonstrates that our technique can produce UWB waveforms with frequency utilization far surpassing the other existing signals under arbitrary spectral mask conditions. Compared to other orthogonality design schemes, the designed pulses can maintain mutual orthogonality without any penalty on frequency utilization, and hence, are much superior in a WDMA network, especially with synchronization deviations. Keywords: UWB-IR sensors; waveform design; orthogonality; waveform division multiple access Sensors 2010, 10 11039 1. Introduction Ultra-wideband impulse radio (UWB-IR) is a promising technique in short-range high-data-rate communication scenarios, such as wireless personal area networks (WPANs) [1]. Meanwhile, UWB- IR sensors have also been employed in military applications such as high-precision radar and through- wall target detection owing to their exceptional multipath resolution and material penetration capability [2-5]. Most recently, the emerging body area network (BAN) field also considers UWB as an appealing solution for health monitoring. These advantages of UWB-IR are mainly attributed to the enormous bandwidth of its transmitted pulses, which may occupy several gigahertz (GHz). However, on the other side, UWB also has long been confronted with rigorous application restrictions, because of its potential interference to other existing vulnerable wireless systems, such as Global Positioning System (GPS) and Universal Mobile Telecommunications System (UMTS) [6]. The first UWB emission mask was set out by U.S. Federal Communications Commission (FCC) in 2002, accompanying the authorization of its unlicensed use in the 3.1–10.6 GHz band [7]. For thorough spectral compatibility between those systems sharing the same band, the released UWB emission limits are very strict; for example, the FCC allowable equivalent isotropically radiated power (EIRP) for UWB transmitted signals is below −41.3 dBm/MHz. Hence, with respect to this EIRP mask, only when the transmitted pulses make full use of the regulated spectral energy, can a sufficiently high signal to noise ratio (SNR) be obtained in UWB receivers, which in turn enhances transmission reliability. Although the traditional Gaussian monocycle has been widely used in the early stages because of its simple realization, its frequency utilization is quite limited [8], so many publications have focused on this issue in recent years. In [9,10], Parr constructed an equivalent channel matrix from the sampled mask, and generated orthogonal UWB pulses from its dominant eigenvectors. However, the frequency utilization remains rather low, and the required 64 GHz sampling frequency makes it comparatively hard to implement. The Finite Impulse Response (FIR) filter based technique adopting Parks-McClellan (PM) algorithm has been presented in [11]. Unfortunately, the spectral mismatch between the designed PSD and emission mask is remarkable near the sharp spectral discontinuities. Davidson et al. [12] applied linear matrix inequalities (LMI) theory to design FIR filter, which could conform to piecewise constant and piecewise trigonometric polynomial masks. Later, a FIR-based pulse shaper has been fully extended by using second order cone programming (SOCP) and it achieved relatively high frequency utilization [13,14]. However, their expected filter orders may be comparative large in order to achieve an acceptable frequency utilization, and the pulses still cannot use the lower frequency region (0–0.9 GHz) entirely. In [15], Ohno and Ikegami synthesized an interference mitigation waveform. Such a UWB pulse can use one single band only and its realization is very complicated given the dozens of carrier generators required both in transmitters and receivers. Other UWB waveform optimization techniques, such as the optimal waveform designing based on Gaussian functions or Rayleigh functions, can match the whole spectral mask to some extent [16,18]. Nevertheless, the frequency utilization of these optimal pulses is still far from satisfactory. In addition, modern communication design has gradually paid attention to resolving the spectrum scarcity, so that the orthogonal waveform multiplexing have been widely adopted to further improve the frequency efficiency, which can also eliminate mutual interference or provide Sensors 2010, 10 11040 considerable waveforms diversity gain in UWB sensor networks [19]. Therefore, an orthogonal waveform set becomes indispensable in system design. The Hermite-Gaussian function and wavelet have been introduced to design mutually orthogonal UWB waveforms; however, their frequency utilization cannot been further optimized [20,21]. Although spectrally efficient orthogonal waveforms have been devised based on the FIR filter [13,14], the complexity of this sequential algorithm may grow with the increasing number of orthogonal users. More importantly, the frequency utilization of subsequent derived pulses undergoes an obvious degradation. Besides, these designed orthogonal pulses are rather sensitive to synchronization deviations, which imposes stringent requirements on receiving timing and hence increases complexity [14,20]. In this paper, we propose a novel pulse forming technique for UWB-IR sensors. The frequency domain representation of the emission pulse is firstly derived from the product of a weight vector and the cyclic shift matrix (CSM) constructed from the basis waveforms. As a result, the spectral shaping problem is transformed to an optimization of the corresponding weight vector. With the permission that the designed PSD can temporarily outstrip UWB spectral masks, the design process can be simplified greatly. Later, this preliminary waveform would be further modified iteratively to lower the excess PSD until UWB pulses totally conform to emission constraints. Numerical evaluations indicate that our pulse can match the arbitrary spectral constraint much more completely than the other existing schemes. The proposed structure can also be viewed as a versatile pulse generator which can be efficiently implemented for digital signal processing (DSP). Hence, it can be directly applied to arbitrary UWB masks. We also design UWB waveforms with spectrum notch attenuated nearly 50 dB in specific bands, which is of great significance for cognitive radios (CRs) considering spectral avoidance to primary users. Based on this already proposed algorithm, the constraint on orthogonal waveforms has also been derived. In order to obtain orthogonal pulses, schemes both from time domain and frequency domain have been addressed. We demonstrate that our designed orthogonal waveforms can use spectral mask as entirely as a single pulse. It is shown through analysis and simulation evaluations that the designed orthogonal pulses outperform other UWB waveforms in a WDMA network if mutual interference from nearby sensors is taken into account, especially when the synchronization deviation exists. The rest of this paper is organized as follows: Section 2 elaborates on the design algorithm in detail. The orthogonal UWB pulses with efficient frequency utilization will be analyzed in Section 3. In Section 4, we discuss and evaluate the performance of UWB pulses in WDMA network with different degree of timing accuracy. At last, we conclude the paper in Section 5. 2. UWB Waveform Design In order to eliminate potential interference from UWB sensors to the other vulnerable wireless systems sharing the same frequency band, the emission power of transmitted UWB pulses has been rigorously limited in different frequencies [6]. The regulatory FCC spectral mask for indoor UWB devices can be shown as: Sensors 2010, 10 11041 41.3dBm MHz f[0, 0.96] GHz 75.3dBm MHz f[0.96, 1.61] GHz 53.3dBm MHz f[1.61, 1.99] GHz Mf() FCC 51.3dBm MHz f[1.99, 3.1] GHz
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