# Time Modulated Arrays: From their Origin to Their Utilization in Wireless Communication Systems
## 2 State of the Art
### TMA Design under a Signal Processing Perspective
#### 2.3.2 Towards Using TMAs in Wireless Communication Systems  
None of the above-referenced works analyze in depth, and in a theoretical way, the influence of TMA on digital communication wireless systems. In this sense, the feasibility of TMA for digital communications has been investigated in [72]. This first insight towards the study of the impact of the TMA technique on the transmission of digital signals has focused on a particular family: linear modulations (Chapter 5, [73]). The main reason for this choice is that these signals exhibit the simplest schemes to be considered in any analysis pertaining to digital signal transmission systems. On the other hand, a TMA by itself imposes a nonlinear transformation--derived from the application of periodic pulses to the antenna excitations, as mentioned above--and, therefore, linear modulations avoid the introduction of additional nonlinearities in the communication system. The block diagram in Figure 2 illustrates the continuous-time version of the system under study, in which a linearly modulated digital signal \(s(t)\) is first generated by means of an in-phase and quadrature modulator at carrier \(f_{c}\), and, next, \(s(t)\) is radiated through a TMA that exploits its fundamental pattern assuming a fast decay of the harmonics. Note that we restrict ourselves to the continuous-time model (thus the digital-to-analog converter (DAC) is not included) and that the digital information symbols are generated at a symbol period \(T_{s}\). Accordingly, the restrictions to safeguard the integrity of the signal and the radiated power (useful and SR) under those conditions have been mathematically analyzed and quantified, both in the time and frequency domains. * The referred restrictions are the following: 1. \(f_{0}\ll f_{c}\), with \(f_{0}=1/T_{0}\) being the TMA fundamental frequency and \(f_{c}\) the carrier frequency of the TMA input signal \(s(t)\) (see Figure 2). 2. \(f_{0}>B_{s}\), where \(B_{s}=(1+\rho)/T_{s}\) is the bandwidth of the TMA input signal \(s(t)\), \(T_{s}\) is the symbol period and \(\rho\in[0,1]\) is the so-called roll-off factor when the transmit filter \(p_{\text{TX}}(t)\) corresponds to the well known raised cosine filter [74]. * The radiated power through the TMA is given by: \[P_{\text{rad}}=\mathcal{G}_{\text{TMA}}P_{ui}=\left(\mathcal{G}_{\text{TMA}_{ 0}}+\mathcal{G}_{\text{TMA}_{\text{SR}}}\right)P_{ui},\] (5) where \(P_{ui}=4\pi\mathcal{D}_{u}\) (expressed in watts) represents the power radiated by an isotropic antenna transmitting a linearly modulated equivalent baseband digital signal \(u(t)\in\mathbb{C}\) with a power density \(\mathcal{D}_{u}\) (it is possible to consider \(\mathcal{D}_{u}=E_{s}(4-\rho)/4\), with \(E_{s}\) being the average transmit symbol energy and \(\rho\) the roll-off factor of the raised cosine filter), whereas \(\mathcal{G}_{\text{TMA}}\) represents the TMA power transfer function (dimensionless) accounting for both the array geometry and the time-modulated elements radiating a carrier signal. The \(\mathcal{G}_{\text{TMA}}\) expression coincides with the array total power in (Equation (30), [58]) and is employed to separate the useful power for \(q=0\) (\(\mathcal{G}_{\text{TMA}_{0}}\)) from the harmonic SR losses for \(q\
eq 0\) (\(\mathcal{G}_{\text{TMA}_{\text{SR}}}\)). Once the conditions for faithfully transmitting digital signals over a TMA have been stated, as well as the SR losses characterized, the next step consists in investigating the impact of a TMA on the performance of a digital communication system. Aligned with this idea, the performance --or quality-- of the communication link in which the TMA is involved was studied in [75]. In such a work, the TMA exclusively exploits its fundamental pattern (a pencil beam pattern in this case).