## 1 Introduction
A low-complexity dual-mode OFDM-IM system was proposed in [28], which employed a DL model known as DeepDM constructed through a combined DNN and convolutional neural network (CNN) to identify carrier bits and index bits independently. The authors of [29] proposed an index-bit detection neural network for OFDM-IM that incorporated fully connected layers and an inception module to effectively manage different modulation settings. In [30], the authors presented a DL-based index bit estimator (IE-DNN) for active LED index detection in visible-light communication systems. By employing fully connected or convolutional layers, IE-DNN significantly reduces the index error rate (IER) and BER with acceptable complexity. In [31], the authors presented a CNN-based detection framework for OFDM-IM systems. This framework uses convolutional layers to effectively identify indices by converting incoming symbols to polar coordinates, creating 2D matrices. In [32], the authors proposed a multiple-input-multiple-output OFDM-IM system using IMNet, a non-iterative detector. The IMNet design combines two subnetswith the conventional least squares method to recover the transmitted signal. In [33], a transformer-based detector called TransIM was proposed. The structure of the transformer adds a great deal of complexity to TransIM. In an earlier work [34], we presented a long short-term memory (LSTM)-based detector for OFDM-IM systems. Although we mostly concentrated on perfect channel conditions in that study, we also assessed BER performance under uncertain channel state information (CSI) settings. Interestingly, under imperfect CSI conditions, our previous experiment outperformed the ML, GD, and DeepIM detectors at higher SNR levels while showing comparable performance at lower SNR levels. CNN-based models can effectively learn and extract features from received signals [35]. Their ability to capture spatial hierarchies enhances the detection of active subcarriers, enabling more accurate index identification in OFDM-IM systems. The translation invariance of CNNs ensures consistent performance across varying signal positions, while their parameter efficiency reduces the risk of overfitting [31]. Furthermore, by incorporating dependencies from both past and future contexts, bidirectional LSTM (Bi-LSTM) models enhance sequential data processing. They address the vanishing gradient issue, enabling effective learning of long-range relationships, and provide parallel processing, which increases training efficiency [36; 37]. In this paper, we propose a hybrid DL (HDL)-based OFDM-IM system designed to operate under uncertain CSI conditions. The proposed HDL detector integrates a one-dimensional CNN (1D-CNN) with a Bi-LSTM model. The 1D-CNN model extracts spatial information from the received signal, focusing on patterns associated with the activated subcarriers by analyzing the received symbols in the OFDM-IM system. This step enhances the model's capacity to differentiate between various indices in the input data. The Bi-LSTM then processes these features, capturing temporal dependencies in the signal by considering both past and future information. This combined approach leverages spatial and temporal insights, significantly improving the OFDM-IM system's BER performance as well as its adaptability to signal variations, resulting in more accurate index detection. We evaluate the BER performance of the proposed model across different signal-to-noise ratios (SNRs) for the OFDM-IM system under imperfect CSI conditions. Additionally, we assess the BER for various optimizers and equalizers. We determine the throughput and spectral efficiency (SE) to further illustrate the resilience of the suggested HDL-based OFDM-IM system. Our simulation results demonstrate that the proposed model outperforms traditional detectors as well as other DL-based detectors. The key contributions of this paper are summarized as follows:  
* We introduce an HDL-based OFDM-IM system that operates under uncertain CSI conditions.