# Mixed-Carrier Communication for Technology Division Multiplexing
## 2 Transmitter and Receiver Design  
As the MCC unified waveform supports simultaneous multiple modulations, it requires a design procedure that avoids possible interference between the signal components. Additionally, MCC is composed to be supporting multiple receiver complexities. In this section, the transmitter and receiver design is explained. As shown in Figure 1, there are two separate streams of bits to be communicating with both high- and low-speed devices. The high-speed bits are OFDM modulated, while the low-speed bits are distributed between \(L_{1}\)- beacon position modulation (\(L_{1}\)-BPM) and \(L_{2}\)- beacon phase-shift keying (\(L_{2}\)-BnPSK) modulation paths. As to comply with dimming control, MCC is designed upon a PWM-like envelope. According to Equations (1) and (2), a sinusoidal beacon \(b(t)\) is \(L_{2}\)-BnPSK modulated and sampled; i.e., \(b_{s}(t)\), at \(T_{\text{PWM}}\) intervals:  
\[b(t)=\sin\big{(}\frac{2\pi t}{T_{b}}+\theta_{n}\big{)} \tag{1}\]  
where  
\[\theta_{n}=(2n-1)\frac{\pi}{L_{2}}\ \,\ \ n=1,2,...,L_{2}\ \ \ \text{for}\ L_{2}\text{-BnPSK},\ L_{2}>2,\]  
\[\theta_{n}=(1-n)\pi\ \,\ \ n=0,1\ \ \ \text{for}\ 2\text{-BnPSK}\]\[b_{\rm s}(t)=\sum_{n=0}^{L_{2}}b(nT_{\rm PWM})\;\delta(t-nT_{\rm PWM}) \tag{2}\]  
In Equation (3), beacon PWM sampling is explained, where every beacon sample is represented by a specific PWM duty cycle according to Equation (4). The \(L_{2}\)-BnPSK modulated PWM-sampled beacon is composed of reshaped ACO-OFDM samples to formulate a PWM-like envelope as shown in Equation (4). In Figure 1, the high-speed bits modulation path to generate ACO-OFDM samples is shown. The bits are modulated using a QAM-modulator; then, hermitian symmetry is applied before the inverse fast Fourier transform (IFFT) block to ensure a real output. All negative samples are clipped to generate positive samples only. Due to the half-wave symmetry property of ACO-OFDM, clipping the negative samples only adds clipping noise to the even sub-carriers, whereas ACO-OFDM has only the odd sub-carriers active. MCC can still be generated using different optical OFDM modulation variations:  
\[b_{\rm PWM}(t)=\sum_{n=0}^{L_{2}}b_{n-\rm PWM}(t-nT_{\rm PWM}) \tag{3}\]  
\[b_{n-\rm PWM}= \begin{cases}2L_{1}P+\sum_{k=1}^{l}x_{k-\rm ACO-OFDM}(t),&0\leq t \leq T_{H}(n)\\ \sum_{k=i+1}^{\gamma_{f}-i}x_{k-\rm ACO-OFDM}(t),&T_{H}(n)<t\leq T_{\rm PWM} \end{cases}  \tag{4}\]  
where  
\[T_{H}(n)=\frac{b(nT_{\rm PWM})-b_{s-\rm min}(t)}{b_{s-\rm max}(t)-b_{s-\rm min }(t)}\;T_{\rm PWM},\]  
\(\gamma_{f}=T_{\rm PWM}/T_{\rm OFDM}\) and \(i\) is the number of OFDM symbols per the on duration of the PWM cycle, \(T_{H}(n)\). It is essential to note that \(x_{k-\rm ACO-OFDM}(t)\) represents negative ACO-OFDM, where positive samples are clipped rather than the negative samples being clipped as in conventional ACO-OFDM, \(x_{k-\rm ACO-OFDM}(t)\). Reshaping \(x_{k-\rm ACO-OFDM}(t)\) within the on duration of the PWM duty cycle, \(T_{H}(n)\), allows the OFDM analog samples to be within the PWM dynamic range. Due to the half-wave symmetry property, a conventional ACO-OFDM receiver can still be used to detect both \(x_{k-\rm ACO-OFDM}(t)\) and \(x_{k-\rm ACO-OFDM}(t)\) within an MCC envelope [22]. To ensure the orthogonality between OFDM sub-carriers and PWM harmonics, the minimum on duration within a PWM sample, \(T_{H}(n)_{\rm min}\), of duty cycle, \(d(n)_{\rm min}\), should allocate an integer number of OFDM symbols as follows:  
\[T_{H}(n)_{\rm min}=\frac{d(n)_{\rm min}\;T_{b}}{L_{2}}=i\;T_{\rm OFDM}\; \forall i\in\mathbb{Z}^{+} \tag{5}\]  
Figure 1: MCC transmitter. As illustrated in Figure 1, the beacon position is modulated within a PWM-like envelope to represent the \(L_{1}\)-BPM bits.