## 1 Introduction
In the literature, the SM-LDM system model was proposed and studied from different and related perspectives as summarized in Table 1. In [13; 14], the authors proposed SM-LDM for a digital TV scenario, and the mutual information (MI) analysis is applied to evaluate the SE considering the two types of inputs: Gaussian and finite alphabet (FA). In [15], the power ratio distributions for the SM-LDM layers are optimized based on the gradient descent algorithm. Additionally, the concavity analysis is applied for SE evaluation. In [16], the SM-LDM is introduced to the terrestrial broadcasting system, and the SE is analyzed and compared to the single antenna LDM as well as LDM with spatial multiplexing (SMX)-LDM and SM with time/frequency division multiplexing. The average symbol error rate, pairwise error probability (PEP), and SE were analyzed for the SM-LDM in the broadcasting/multicasting systems of [17] for correlated Rayleigh fading channels. Then, the PA problem was formulated based on maximizing the SE with quality-of-service constraints. In [19], the NOMA-SM system model was proposed and classified in terms of the number of active transmit antennas into single-RF and multi-RF. A PA technique is introduced based on equalizing the signal-to-interference-plus-noise ratios (SINRs). The users either independently or cooperatively select their antenna for transmission. SE was analyzed for the users using MI analysis for Gaussian and FA inputs. By inspecting the most related work, the power ratios are preassigned and kept constant in [13; 14; 16]. Though it is low complexity, Pre-PA does not take into consideration the dynamic change of the SINRs. The SINRs are highly unbalanced in LDM systems due to applying different modulation schemes. The \(LL\) employs high-order modulation, and accordingly, it has a small squared minimum Euclidean distance (SMED) between the constellation points. Low-order modulation with a high SMED, on the other hand, is utilized by the \(UL\) to achieve reliable communication. As a result, using the SMED factor is critical to determining the proper power ratios that compensate for the difference between the SINRs and achieve improved BER fairness between the layers. Even though [15; 17] proposed PA algorithms instead of the Pre-PA, the data rate and SMED differences between the layers are not taken into consideration. The sum rate and total SE were investigated, but not the individual layer rates or BER performance. Moreover, in [19] the users should have identical configurations in terms of modulation order and number of receive antennas to obtain BER fairness. On the other hand, in [13; 14; 15; 16; 17] each layer chooses its own active transmit antenna independently. Furthermore, each layer provides its service by broadcasting a modulation symbol, which necessitates SIC at the \(LL\) and results in increased inter-layer interference (ILI). It improves SE, but it requires two RF chains (thinking of two layers, \(UL\) and \(LL\)), which reduces EE and adds hardware complexity. This study aims to develop the SM-LDM system from two perspectives: power ratio distribution and the transceiver system model. Ineffective PA strategies can cause significant interference, unequal rate distribution between paired layers (i.e., less fairness), system outages due to SIC failure, and a decline in performance. As a result, an appropriate PA is required to improve system performance. Furthermore, it is essential to enhance the practicality of the SM-LDM transceiver system paradigm and achieve seamless adoption of SM and LDM technologies. The following are the main contributions of this research:  
* Propose a new power allocation method identified as biased-PA (Bi-PA) for the SM-LDM system capable of improving BER fairness between layers and maximizing sum-rate, particularly in low and intermediate SNR regions. Bi-PA accomplishes this by adaptively calculating power ratios based on SINR balance and prioritizing the layer with the lowest SMED between modulation symbols.