## 1 Introduction  
Layer division multiplexing (LDM) [1], a power-based non-orthogonal multiple access (NOMA) technology, is gaining popularity in a variety of wireless applications to deliver robust high-definition services [2; 3; 4]. Recently, the advanced television systems committee (ATSC) 3.0 standard applied LDM for broadcasting systems [5; 6; 7; 8; 9; 10]. It allows for a high-capacity link for stationary users as well as a robust configuration for mobile users. Multilayer signals in LDM carry services with varying requirements for throughput and robustness to share resources [7]. Moreover, it has been shown that spectral efficiency (SE)is improved by the distribution of power to individual services, making LDM superior to both time/frequency division multiplexing [11]. There are commonly two layers in LDM broadcasting systems: the upper layer (_UL_) and the lower layer (_LL_). The _UL_ delivers low-data rate service with a robust transmission constellation for the mobile receiver via low-order modulation techniques. Alternatively, the _LL_, having better channel conditions, provides high data rate service for the fixed receiver via high modulation order techniques. In contrast to NOMA users, who are allowed to make use of the same kind of modulation strategy, LDM services must be delivered using a variety of alternative modulation constellations [1; 2]. One example of this would be QPSK for _UL_ and 64-QAM for _LL_. Considering a downlink system, the base station (BS) maps the data of both layers to their corresponding constellation symbols. Then, with different power levels, a superimposed signal of these symbols is transmitted. Typically, the _UL_ receives a larger share of the total transmitted power than the _LL_. On the receiver's side, the _LL_ receiver cancels the _UL_ signal before detecting its data using successive interference cancellation (SIC). The _UL_ receiver, on the other hand, decodes its data directly and treats the portion received from LL as Gaussian noise [7]. LDM has been combined with several technologies [4; 12]. Among these, LDM that makes use of spatial modulation (SM) has shown promise in comparison to conventional LDM [13; 14; 15; 16; 17] due to its potential for more SE, lower energy consumption, and easier installation. SM is a state-of-the-art multiple-input multiple-output (MIMO) antenna technology that was designed to address issues with traditional MIMO systems, including spatial multiplexing and space-time coding. It is worthwhile to point out that the SM concept has been extended to an index modulation and implemented into a wide range of technologies [18; 19; 20]. In SM [21; 22], only one antenna is active at a time, which simplifies the hardware and reduces the amount of power generated by the radio frequency (RF) chains. Other antennas transmit no power, reducing inter-channel interference and alleviating the need for antenna synchronization. Furthermore, the index of the active antenna is selected through the user information bits, allowing for a high transmission rate, which becomes even more impressive in the case of massive MIMO. In SM, the data are split into two parts: antenna selection (AS) and symbol selection (SS). The SS bits determine the standard QAM/PSK modulation, while the AS bits specify the index of the active antenna. When the whole information bits are utilized for AS bits solely, a space shift keying (SSK) signal is transmitted [23]. This research aims to improve the efficacy of integrated SM-LDM technologies by proposing new power allocation (PA) and antenna selection (AS) methods. The distribution of the BS transmit power among the LDM layers is critical in determining their achievable rates, detection capability, and overall SE and bit error rate (BER) system performance. Further, the PA and AS techniques demonstrate their usefulness for MIMO- [24; 25] and SM-based related systems [26], particularly in terms of improving energy efficiency and lowering costs. In AS, one or a subset of antennas is active, requiring fewer RF chains.