# On Coding and Decoding Reconfigurable Radiation Pattern Modulation Symbols
## 1 Introduction  
We are in a time of instant communication. Users require ever-increasing speed, power, and availability. Communication systems have remained almost unchanged since the invention of the superheterodyne receiver [1] and the introduction of coding [2]. Artificial intelligence, remote surgeries, virtual reality, autonomous cars, the increased need for remote working due in particular to healthcare issues (e.g., the COVID-19 pandemic), and the internet of things (IoT) are among the avenues that revolutionize the technology of this century. Techniques such as enhanced multiple-input and multiple-output (MIMO) systems, millimeter-wave (mmWave), and controllable electromagnetic environments are proposed to be standardized in the coming years. While MIMO systems have become essential parts of almost all modern communication systems [3, 4], there are scenarios where the number of used antennas cannot be massive. New modulation methodologies need to be implemented to minimize the number of components while maximizing the capacity of the communication system. The index modulation (IM) technique, which maximizes the amount of information that is extracted from the building blocks of the communication chain, is a strong candidate for the communication revolution due to its hardware simplicity [5, 6, 7]. IM has been investigated since the beginning of the millennium [8, 9, 10, 11, 12], attracting even more attention in recent years. This technique focuses on the states of the building blocks rather than the classical parameters from the signal, e.g., amplitude, phase, and/or frequency. IM schemes can alternate the ON and OFF states of the communication blocks to encode data; antennas, RF diodes, RF mirrors, signal powers, sub-carriers, modulation types, and loads are typical examples of communication blocks that can be used as IM [13, 14, 15, 16]. In the same vein, one of the most promising types of IM schemes is reconfigurable radiation patterns modulation (RRFM) [17, 18]; the information bits areencoded onto the radiation patterns of reconfigurable antenna arrays, programmable metasurfaces [19; 20], or reconfigurable antennas [21; 22]. Most of the current effort has focused on the device that emits the radiation patterns rather than measuring the emitted pattern.  
In this work, we propose a methodology for characterizing RRPM systems under realistic conditions. In fact, in the current literature, radiation patterns from multiple sources (reconfigurable-antennas, metasurfaces) are measured using an anechoic chamber with a turntable surrounded by a high number of antennas that results in a high-resolution reconstruction of the transmitted symbols. In this paper, we assume a realistic scenario instead, with a limited number of receiving antennas that partially reconstruct the radiation symbols. For instance, one receiving antenna is needed for measuring a point \(P(\theta,\ \phi)\) in the far-field; a low density of receiving antennas will result in a sparse symbol reconstruction. Under these restrictions of direction and receiving antennas, the transmitted symbols must be optimized in order to reduce the probability of error. A methodology for selecting the radiation symbols with the minimum probability of error to be transmitted is developed for a realistic scenario. The symbols are transmitted over a noisy simulated channel with a minimal number of receiving antennas, positioned at specific fractions of the study domain (spherical coordinates). Afterward, the bit-error-rate (BER) is calculated and quantified for each case as the leading figure of merit.  
The remainder of this paper is organized as follows: Section 2 gives the theoretical background of this work. Section 3 introduces the algorithm for smart radiation pattern symbol selection and details the BER Monte-Carlo simulations for different scenarios of measured radiation patterns. Section 4 gives a short discussion and some concluding remarks on the results obtained.