## 4 Demand Side Management System under Evaluation
### NB-PLC Technique for Demand Side Management  
The orthogonal frequency division multiplexing (OFDM) technique is used to improve the proposed NB-PLC-based DSM system [41; 42]. OFDM has the ability to provide increased an data rate and enhanced immunity against EMI. The process of OFDM will transform NB-PLC line frequency selection into a flat fading parallel channel using a narrowband. The relationship between frequency domain and time domain for an OFDM system can be seen. Overall, the OFDM systems's efficiency can be enhanced using signal collision avoidance concept. This process enables the faintest signal in one frequency domain to be the sharpest in another sub-carrier frequency domain. The OFDM spectrum has multiple subcarriers that are orthogonal and can use the methodologies of shift keying of frequency, phase, or amplitude. Each subcarrier can handle a specific amount of data rate, error correction code, and error detection code [39; 43]. The receiver filters the OFDM signal to minimize the noise and the original signal is retrieved after demodulation. The modulation of subcarriers is performed by M-phase shift keying (M-PSK) or quadrature amplitude modulation (QAM). The expression for M-PSK is given as  
\[S_{i}(t)= \sqrt{\frac{2E_{s}}{T_{s}}}\cos\left(2\pi f_{c}+\frac{2\pi(i-1)}{ M}\right)\quad 0\leq t\leq T_{s}\] \[i=1,2,\cdots,M \tag{15}\]  
here \(T_{s}\), \(E_{s}\) and \(f_{c}\) represent guard time, energy, and carrier frequency, respectively. The phase angle of carrier frequencies can be obtained using the following relation. \[\theta_{i}=\frac{2(i-1)\pi}{M}\ \ i=1,2,\cdots,M. \tag{16}\]  
In QAM, the \(n\)th symbol is given by  
\[S_{n}(t)= \sqrt{\frac{2E}{T}}a_{n}\cos(2\pi f_{c}t)-\sqrt{\frac{2E}{T}}b_{ n}\sin(2\pi f_{c}t)\] \[0\leq t\leq T\ \ \ n=0,\pm 1,\pm 2,\cdots \tag{17}\]  
where minimum energy of QAM is denoted by \(E\) whereas \(a_{n}\) and \(b_{n}\) represent the \(n\)th symbol energy given by  
\[a_{n},b_{n}=\pm a,\pm 3a,\cdots,\pm(\log_{2}M-1)a. \tag{18}\]  
The electric power lines can be very hostile for NB-PLC systems. Many issues like multipath effect, dispersion, and time and frequency selections with multi-reflections can have an adverse effect on the performance of the NB-PLC communication system [44; 45; 46]. Especially time and frequency selection and dispersion have an enormous impact on NB-PLC systems, because these are very common issues and are present in every wireless communication system. Time dispersion can impact the NB-PLC system by inducing more delays and phase-shifting duplications. Another important factor affecting the performance of NB-PLC is noise. Noise can be either of two types: background noise and impulsive noise. Both types of noise have a significant impact on the NB-PLC system's efficiency. Background noise is further categorized into colored and narrowband noise, while the impulsive noise can be divided into mainly two types: periodic (synchronous or asynchronous) and aperiodic. The NB-PLC channels are useless for control signals, especially if the signal power is less than the noise power. Signal to noise ratio (SNR) is used to determine the quality of NB-PLC control signals using the following relation [47]. \[\mathrm{SNR}=10\log\biggl{(}\frac{P_{S}}{P_{n}}\biggr{)} \tag{19}\]  
where \(P_{S}\) represents the power of the signal and \(P_{N}\) represents the power of noise. By considering noise with Gaussian distribution with 0 mean value, the bit error rate (BER) of binary signal can be given as  
\[Q\biggl{(}\frac{2A}{\sigma}\biggr{)}=\int_{2A}^{\infty}\frac{1}{\sqrt[3]{2\pi \sigma^{2}}}e^{\frac{-y^{2}}{2\sigma^{2}}}dy \tag{20}\]  
where \(A\) is the amplitude and \(\sigma\) denotes the standard deviation. The square root of SNR is represented by \(\frac{2A}{\sigma}\) therefore bit error rate (BER) of transmitted signal is a function of SNR.