This work proposes a novel and efficient quadstream BiLSTM-Attention network, abbreviated as QSLA network, for robust automatic modulation classification (AMC) of wireless signals. The proposed model exploits multiple representations of the wireless signal as inputs to the network and the feature extraction process combines convolutional and BiLSTM layers for processing the spatial and temporal features of the signal, respectively. An attention layer is used after the BiLSTM layer to emphasize the important temporal features. The experimental results on the recent and realistic RML22 dataset demonstrate the superior performance of the proposed model with an accuracy up to around 99%. The model is compared with other benchmark models in the literature in terms of classification accuracy, computational complexity, memory usage, and training time to show the effectiveness of our proposed approach.