## 4 Multiple-User UWB System  
For multiple channels, a unique pattern was assigned in order to encode data from each channel. In the proposed work, UWB MHP based on a pulse-encoding scheme is shown for simultaneous communication and higher data density. In the pulse-encoding scheme, instead of using conventional a single Gaussian pulse, a series of analog orthogonal pulses are utilized for simultaneous multi-channel support, and interference-free communication. For n-number of MHP orthogonal pulses, the channel number has been increased to \(n(n-1)\). Hence, a unique pattern sequence has been developed by encoding the MHP orthogonal pulses to transmit binary high bits for each channel. By using 4 orthogonal pulses the proposed scheme can generate distinctive pattern sequences for 12 channels. The proposed scheme is different than the IFFT-based Walsh-Hadamard orthogonal code generation [60; 61; 62; 63; 64; 65; 66; 67; 68; 69] where for a Hadamard matrix size of n results in \(2^{n}\) number of channels. The main novelty of the proposed scheme is the reduced computational burden to generate the pulse-sequence as compared to the IFFT-based transform to generate the orthogonal vectors. With 4 orthogonal pulses, the pattern will be a sequence of 4 unique orthogonal pulses. The receiver will be able to determine if a channel is transmitting binary 1 or 0 by matching the pattern, as each high bit (binary 1) from the channels will be represented by a unique sequence of 4 orthogonal pulses. The number of unique patterns that can be generated for a given number of orthogonal pulses is directed by,  
\[N=n(n-1) \tag{3}\]  
where \(n\) is the number of orthogonal signals. For \(n\) numbers of orthogonal pulse, each channel will have \(n\) signal in the pattern. Tables 11-13 presents the different combinations of unique patterns for different number of orthogonal pulses. As governed by the Equation (3), the number of unique patterns for 2, 3, and 4 orthogonal pulses is 2, 6, and 12 respectively. With 4 orthogonal pulses, 12 channels can be generated with 4-bit unique patterns. Each high bit (binary 1) from the channels will be represented by 4-bit sequence pattern as shown in Table 13. Each high bit from the channels will be spread into 4-bit unique sequences. This spread bits from all the channels will be added in time, resulting in a total of only 4 composite pulses from all the channels. The added 4 composite pulses will be transmitted in sequence. The transmitter architecture with 4 orthogonal pulses is shown in Figure 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**S.N.** & **Data** & **Pulse Representation** \\ \hline
1. & 0000 & No pulse \\
2. & 0001 & \(MHP_{0}\) \\
3. & 0010 & \(MHP_{1}\) \\
4. & 0011 & \(MHP_{2}\) \\
5. & 0100 & \(MHP_{3}\) \\
6. & 0101 & \(MHP_{0,1}\) \\
7. & 0110 & \(MHP_{0,2}\) \\
8. & 0111 & \(MHP_{0,3}\) \\
9. & 1000 & \(MHP_{1,2}\) \\
10. & 1001 & \(MHP_{1,3}\) \\
11. & 1010 & \(MHP_{2,3}\) \\
12. & 1011 & \(MHP_{0,1,2}\) \\
13. & 1100 & \(MHP_{0,1,3}\) \\
14. & 1101 & \(MHP_{0,2,3}\) \\
15. & 1110 & \(MHP_{1,2,3}\) \\
16. & 1111 & \(MHP_{0,1,2,3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Proposed scheme for data transmission using 4 orthogonal pulses in a single-user scenario. The Figure 3 shows the logic of how the core section of the transmitter works for the proposed modulation scheme with 4 orthogonal pulses. Each bit from all the channels will be represented by the unique sequence of 4 orthogonal pulses. For instance, binary data '1' from channel 1 is represented by a sequence of MHP: 0, 1, 2, and 3. These individual bits from all the channels are then added in time in their respective positions by the composite symbol generator. These composite pulses contain the sum of different orthogonal pulses from all the channels, which are transmitted subsequently in the sequence illustrated in Figure 3. This will result in a total of 4 composite pulses for final transmission.