Improving the UWB Pulseshaper Design Using Nonconstant Upper Bounds in Semidefinite Programming

A critical obstacle for ultra-wideband (UWB) communications is conformity to restrictions set on the allowed interference to other wireless devices. To this end, UWB signals have to comply with stringent constraints on their emitted power, defined by the Federal Communications Commission spectral mask. Different UWB pulseshaper designs have been studied to meet the spectral mask, out of which an approach based on digital finite impulse response filter design via semidefinite programming has stood out. However, so far this approach has assumed an ideal basic analog pulse to use piece-wise constant constraints for the digital filter design. Since any practical analog pulse does not have a flat spectrum, using piece-wise constant constraints leads to considerable power loss. Avoiding such a loss has motivated us to implement the exact constraints through nonconstant piece-wise continuous bounds. Relative to the design assuming an ideal basic analog pulse, our design examples show that the transmission power can be enhanced considerably while obeying the spectral mask. Such an improvement comes with no extra cost of implementation complexity.