Nowadays, Smart Home Systems (SHSs) have emerged as an important technology towards employing the power of the wireless media and IoT devices. Devices in SHSs interact with numerous smart applications running simultaneously with different platforms to deliver required services. Such ubiquitous systems often serve as a potential platform for escalating malicious entities to launch cyber attacks such as Distributed Denial of Service (DDoS) attacks. The expense of DDoS attacks makes it critical to develop counter-measures that can effectively stop the attack and quickly identify the attacker(s). Thus, one of the main challenges of these network monitoring is the ability to quickly and accurately detect DDoS attacks. To address this problem, we propose a Deep Learning (DL)-based method to classify smart home network traffic into two classes, namely normal and malicious. Training the proposed model with normal and DDoS attack data to classify attack instances. In order to overcome the problem of the lack of data, as is often the case, synthetic data has been generated using a Conditional Tabular Generative Adversarial Network (CTGAN). It is then used to train a DDoS attack detection model using an API functional model in order to maximise the performance and enhance detection rates. Results of experiments demonstrate that the proposed method tends to outperform existing approaches with an accuracy rate of 99.98%.