## 1 Introduction  
In recent times, ultra-wide band (UWB) communication technology has become widely used in wireless sensing applications such as structural health monitoring, patient health care monitoring, military surveillance, and smart homes, etc. Owing to its attractive features like lower power consumption, its power spectrum below the noise floor, and its consistency with preexisting wireless technologies, there is a shift of interest among researchers towards the pulse-based UWB communication since narrow-band communication for WSN is afflicted with channel impairments and bandwidth constraints. In a UWB system, the narrow-band signal is a major interferer; however, a significant number of articles have been reported to mitigate these problems [1; 2; 3; 4; 5]. A lot of work has been put in towards developing innovative techniques for pulse set generation and modulation for UWB systems. Pulse-position amplitude modulation (PPAM) [6], biorthogonal-pulse position modulation (BPPM) [7], and OOK-PSM [8] are proposed in several works in the literature to achieve better system performance using combined modulation techniques with higher data rates, less complex receivers, and lower power consumption. The Federal Communications Commission (FCC) defines the regulation of pulse power and spectrum [9]. Different types of pulse shapes are used to obtain desired power and spectral ranges [10; 11]. One of the main drawbacks of the UWB system is the generation of proper orthogonal pulses and their higher derivatives. A modified Hermite pulse (MHP) set generator has been presentedin [12] which uses an efficient technique to generate orthogonal pulses. Similarly, the authors of [13; 14] endorsed the practice of employing orthogonal pulse to increase the data rate in the prevailing UWB communication systems. The authors of [14] used different pulse in different positions to increase the number of information bits to be transmitted, whereas the authors of [13] utilized an orthogonal pulse sequence to encode the information bits. The orthogonal pulses can be added in time and transmitted as a composite pulse to the receiver end. These orthogonal pulses are then put through a correlator which in turn decodes the composition of the symbols. UWB systems offer many advantages over conventional radio communications systems, e.g., low power consumption for transmission and much improved robustness to multipath interference [15]; as a result UWB technology is very suitable for indoor wireless channels that are very prone to multipath interference. Owing to the short time duration of its pulses, multipath components can be differentiated with ease while higher data rates can also be achieved. Different kinds of modulation schemes have already been proposed for obtaining improved data rates, which in general make use of pulse-position modulation (PPM) in addition to the employment of time-hopping sequences. The constraints associated with the Gaussian monopulse have posed many impediments in the generation of new pulses [16; 17; 18; 19; 20]. It has also been observed that the modified Hermite polynomials can be used to generate the pulses that can be implemented in an M-ary modulation scheme [21], which exploits the mutual orthogonality of such polynomials. In this paper a novel M-ary pulse shape modulation (PSM) scheme for UWB communication technology has been proposed in order to enhance the data rate by exploiting the orthogonal properties of the MHP and increase the number of simultaneous data transmissions. The proposed work shows our previously reported orthogonal modified Hermite polynomial (MHP) pulse-based high data density wireless communication. Unlike existing schemes for orthogonal pulse generation, the developed mathematical model offers fewer required functional blocks, reduced system complexity, and enhanced power efficiency. In this work, instead of using a single orthogonal pulse, a series of pulses or a pulse sequence is used to represent each channel or user.