## 2 Composite Pulse Generation  
Traditional Hermite polynomials have been defined by the authors of [22]. For the purpose of generating orthogonal pulses for UWB communications, MHPs have been proposed by pioneering researchers [23; 24]; which permit one particular dynamic system to generate another MHP. Since orthogonal pulses can be transmitted simultaneously without mutual interference, orthogonal pulse set-based IR-UWB systems have the potential to achieve a higher data rate than the conventional IR-UWB systems [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54]. Most of the mathematical functions for the design of orthogonal UWB pulsessuch as the Haar function [55], the modified Hermite polynomial (MHP) function [22; 23; 24; 56], and the prolate spheroidal wave function (PSWF) [57; 58], etc. involve complicated math models and power hungry hardware implementation [59]. MHP pulses, which have lower computational complexity than PSWF-based pulses, possess the properties of orthogonality and nearly-constant pulse widths irrespective of the pulse orders. However, the conventional MHP generation scheme as proposed in [23; 24] involves the second-order derivative and the squared time function, \(t^{2}\), making the pulse generator complicated in computation. In our previously reported article [12], an innovative choice is made by following the coupled first-order dynamics to break down the second-order system as a combination of two first-order systems and sub-GHz operation to reduce the system complexity and power consumption of the orthogonal pulse generation. Owing to the simplified model, there are only 2 integrators, 5 multipliers, 3 adders, and a ramp signal generator in the system which is significantly less complex and power-efficient than the previous works [22]. An efficient mathematical model for MHP set generation has been presented in [12], where the \(n\)th order derivatives of the MHP are given as  
\[\tau h_{n}(t)=-\frac{t}{2\tau}h_{n}(t)+nh_{n-1}(t) \tag{1}\]  
\[\tau\dot{h}_{n-1}(t)=\frac{t}{2\tau}h_{n-1}(t)-h_{n}(t) \tag{2}\]  
The proposed neuromorphic MHP set generator has been implemented in Cadence by virtue of Verilog-AMS. Figure 1 presents the zero--(\(MHP_{0}\)), first--(\(MHP_{1}\)), second--(\(MHP_{2}\)) and third--(\(MHP_{3}\)) order modified Hermite pulses respectively, generated using the pulse set generator proposed in [12]. The \(MHP\) pulse is called the Gaussian mono-pulse. For higher order pulses the generator generates two complimentary pulses of the same order, which is evident in Figure 1.  
The distinguishing features of the orthogonal pulses being added up in the time domain and the successful recovery of the composition of the composite pulses make it possible to both boost the data  
Figure 1: Combined plots of modified Hermite polynomial (MHP) order 0, 1, 2 and 3 from the generator circuit (pulse width = 10 ns). rate and increase the number of channels for simultaneous transmission. Instead of transmitting the individual orthogonal pulses and modulating in the pulse polarity, position, and phase, this paper proposes the transmission of the composite pulse and modulation of the information in pulse shape. With the proposed scheme of data modulation for \(n\) number of orthogonal pulses, the data rate in the single-user scenario was increased by \(n\) folds and in the case of the multi-user scenario, it supported \(n(n-1)\) channels for simultaneous data transmission. Correlation analysis was performed using MATLAB in order to check the orthogonality of the generated pulses. Tables 1-3 present the correlation values between the orthogonal signals with pulse width of 6 ns, 10 ns, and 18 ns, respectively. The correlation value ranges from \(-1\) to \(1\), where \(1\) implies that there is a perfect correlation between the signals, \(0\) implies that there is no correlation between the signals and \(-1\) implies that the signals are just opposite in nature.