# Parallel Complex Quadrature Spatial Modulation
## 1 Introduction  
Multiple-input multiple-output (MIMO) techniques have the potential to meet the high data rate demands of the future wireless communication generations [1]. Index modulation (IM) is a group of MIMO techniques that utilizes the indices of available communication systems' resources to convey information bits to the receiver [2]. These indices can be physical antennas [3], spreading codes [4], polarities [5], sub-carriers [6], rotation angles [7], and virtual channels [8], among others. At each channel use, only one or a subset of a given resources is activated. Therefore, IM techniques provide an energy efficient advantage to the communication systems over the conventional spatial multiplexing MIMO. Spatial modulation (SM) is an IM technique, where only one antenna is activated to transmit a quadrature amplitude modulation (QAM)/phase shift keying (PSK) signal symbol at each channel use [3, 9]. Both the antenna index and signal symbol convey information to the receiver. Therefore, the SM needs only a single radio frequency (RF) chain at the transmitter and the system avoids inter-channel interference. A drawback of the SM is the exponential growth of the number of transmit antennas to increase the spectral efficiency. Several SM schemes were proposed to improve the spectral efficiency while keeping the transmitter requirements relatively simple. Generalized spatial modulation (GSM) reduces the number of required transmit antennas to achieve a given spectral efficiency by transmitting a signal symbol from a combination of two or more transmit antennas at each channel use [10]. Multiple active SM (MA-SM) uses antenna combinations to transmit independent signal symbols from each active antenna [11]. As such, MA-SM compromises the system's complexity to achieve higher multiplexing gain. Parallel SM (PSM) splits the antenna set into equal-size subsets to transmit a single signal symbol [12; 13] or independent signal symbols [14; 15] from each antenna subset. The constellation design of the PSM with one signal symbol is discussed in [16]. Quadrature spatial modulation (QSM) exploits the in-phase and quadrature component of the transmit antennas to convey additional information through the spatial dimension [17]. At each channel use, the real and imaginary part of a modulated symbol is transmitted on the in-phase and quadrature component of any of the transmit antennas, respectively. The parallel implementation of the QSM with one symbol and independent symbols is proposed in [18; 19], respectively. Improved QSM (IQSM) transmits the real and imaginary parts of two signal symbols, respectively, through the in-phase and quadrature dimensions, using combinations of two antennas [20]. Compared to the IQSM, the authors of [21] introduce double QSM and parallel IQSM to reduce the required number of transmit antennas without additional number of RF chains. In complex QSM (CQSM), two complex symbols are transmitted through any available transmit antennas, at each channel use [22]. To avoid ambiguity at the receiver, the first and second signal symbol is drawn from a conventional QAM/PSK constellation and an optimally rotated one, respectively. The performance of the CQSM was improved in [23], and the constellation design of the improved CQSM was investigated in [24]. Moreover, generalized implementations of the CQSM was proposed in [25]. To further exploit the benefits of the CQSM system, a parallel CQSM (PCQSM) is proposed in this paper. PCQSM divides the group of transmit antennas into equal-size subgroups to apply the CQSM in each group independently, using the same two signal symbols. As such, PCQSM requires two RF chains, keeping the same CQSM hardware requirements. Similar to the CQSM, the signal symbols are drawn from distinct constellations, where the second constellation is a rotated version of the first. The optimal rotation angles that minimize the error rate are obtained offline through extensive Monte Carlo simulations for each system configuration. The merits of the PCQSM are summarized in the following.