With transmit power spectra strictly limited by regulatory spectral masks, the emerging ultra-wideband (UWB) communication systems call for judicious pulse shape design in order to achieve optimal spectrum utilization, spectral mask compatibility, and coexistence with other wireless services. Meanwhile, orthogonal pulse sets are often desired in order to apply high-rate multidimensional modulation and (carrier-free) orthogonal frequency-division multiple access. Motivated by these considerations, we suggest a digital finite impulse response (FIR) filter approach to synthesizing UWB pulses and propose filter design techniques by which optimal waveforms that satisfy the spectral mask can be efficiently obtained. For single pulse design, we develop a convex formulation for the design of the FIR filter coefficients that maximize the spectrum utilization efficiency in terms of both the bandwidth and power allowed by the spectral mask. For orthogonal pulse design, a sequential strategy is derived to formulate the overall pulse design problem as a set of convex subproblems, which are then solved in a sequential manner to yield a set of mutually orthogonal pulses. Our design techniques not only provide waveforms with high spectrum utilization and guaranteed spectral mask compliance but also permit simple modifications that can accommodate several other system objectives.
Bibliographical noteFunding Information:
Manuscript received August 27, 2004; revised June 16, 2005. The work of Z. Tian was supported by the National Science Foundation (NSF) under Grant CCR-0238174. The work of T. N. Davidson was supported by NSERC under a Discovery Grant. The work of G. B. Giannakis was supported by ARL/CTA under Grant DAAD19-01-2-011 and by NSF under Grant EIA-0324804. This paper was presented in part at the IEEE ICASSP Conference, Montreal, QC, Canada, May 2004, and the IEEE SPAWC Conference, Lisbon, Portugal, July 2004. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Peter M. Djuric.
- Digital pulse design
- Finite impulse response (FIR) filter
- Ultra-wide-band communications