UWB pulse design using constraint convex sets method

Abstract

In this paper, we propose a constrained convex sets-based method for designing ultra-wideband (UWB) pulse. The UWB pulses designed using earlier proposed methods either do not fit well in UWB spectral mask or require extra processing circuitry for pulses to fit in the UWB spectral mask. The proposed constraint sets-based method is flexible and optimum for the UWB mask. The pulse designed by the proposed method is Federal Communication Commission compliant and has an autocorrelation function similar to the Gaussian pulse. The bit error rate performance of time hopping binary phase shift keying using the proposed method and some of the existing methods such as Norman and Lee pulses and sixth derivative Gaussian pulse is analyzed in additive white Gaussian noise and Saleh-Valenzuela channels. Pulse designed using the proposed method outperforms existing pulse design, and the same is verified through simulations. The proposed algorithm is flexible and can also be used to mitigate narrow band interference, multiband UWB pulse generation and any other Federal Communication Commission (or other regulatory body) compliant spectrum mask by modifying the parameter of the proposed constraint set(s). INTRODUCTIONThe impulse radio ultra-wideband (UWB) technology is being adopted in IEEE 802.15.4 task group for unlicensed short-range high-data rate wireless transmission and can be used for other upcoming applications such as millimeter wave communications. 1 This unlicensed communication technology requires low power and low cost and, hence, can be used in low power wireless devices such as sensor networks, high-data rate wireless local area network, personal area network communication, various imaging and radar systems, and internet-of-things. 2-6 However, the UWB communication pulse design is a crucial and challenging task because pulse should be maximally flat in frequency, and narrow in time domain. Therefore, sinusoidal pulses are not suitable for UWB communications. Generally, convex optimization-based techniques have been used for the UWB pulse design. 7,8 Various UWB pulses are proposed in literature such as Gaussian, Hermite, and Prolate Spheroidal and using combination of orthogonal polynomials in. 4,9 Pulses used in UWB communications should satisfy the US Federal Communication Commission (FCC) spectral mask. 4 The UWB pulse should have minimum narrow band interference; therefore, its compatibility with FCC mask is desirable. The FCC mask compatible pulse can be designed with the help of projection onto the convex sets (POCS). The required convex sets are formulated based on a given a priori information about the UWB pulse. The proposed method in this paper for pulse designing is generic and flexible and, hence, can be easily applied FCC and other than FCC UWB standards, and also can be used for both single-and multiple-user environments. A vast literature on using various methods for UWB pulse design is available; hence, in this section, we review some of the commonly used UWB pulse designs. In Parr et al, 10 the U...

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