## 2 Background on ML-Based Optimisation of Wireless Networks  
The traditional approach for optimising the performance of wireless transceivers uses a divide-and-conquer concept. The transceiver is separated into signal processing blocks performing, e.g., channel equalisation, demodulation and error correction, which are optimised independently of each otherwith limited cross-block considerations [20]. For the optimisation of a signal processing block, well-established mathematical models are often used, derived from extensive research in information theory, signal processing, and statistics for the past many years [21]. Unfortunately, some of the models, despite being very accurate, can be mathematically intractable with a high complexity order for real-time operational use. For instance, MIMO detectors and pre-coders can be optimally designed based on a maximum a posteriori criterion, which, however, involves the solution of NP-hard problems. Hence, only sub-optimal techniques, such as zero forcing equalisation, can be pragmatically used [11]. Some tractable models may be overly simplistic and inadequate to accurately capture all the intricacies in the wireless propagation medium and the non-linearities and imperfections of hardware components [19]. Overall, the existing block-based transceiver structure associated with mathematical optimisation per block compromises the transceiver performance for simplicity and tractability, which AI/ML-based techniques aspire to address. ML can be used to directly optimise the end-to-end performance by treating the entire system as a black box. This is usually referred to in the literature as the pure data-driven technique [19]. The most intuitive way to apply ML to wireless communications is to consider a transceiver as being an (unsupervised) auto-encoder constituted of an encoder and decoder. Then, both the transmitter and receiver can be implemented as feedforward neural networks (NNs) and can be jointly optimised as a single NN, while the communication channel is modelled by inserting extra hidden layers between them, e.g., a single layer adding white Gaussian noise is used in [22]. More complicated channel transfer functions including the tap-delay-line for wideband transmissions, frequency and phase offsets, and unknown time-of-arrival could be modelled by adding more layers [23]. The target in this approach is to train ML algorithms to learn the optimal system design,i.e., the mapping of source symbols to transmitted waveforms along with optimal decoding at the receiver; see Figure 1.  
Implementing the transceiver as an end-to-end (E2E) auto-encoder is attractive, as it essentially alleviates the need for conventional signal processing without compromising performance; in [22,23], the block error rate in AWGN and multi-tap Rayleigh fading channel using auto-encoders is on par with the baseline schemes. Nevertheless, there are still significant unsolved challenges before adopting NN-based auto-encoders in practice, which are summarised below. 1. Training the auto-encoder over all possible source messages is required, which becomes quickly impractical for long code words. Additionally, it was observed that training at a low SNR does not necessarily generalise well at high SNRs [22], while training at multiple SNRs will prohibitively increase the size of required labelled datasets and time to train the NN. 2. The channel and all impairments between the transmitter and receiver must have a known deterministic functional form and be differentiable, which is seldom the case. For instance, the fading channel probabilistically varies over space and time. Furthermore, some impairments may not be differentiable, such as quantisation, or its mathematical representation may be inaccurate (e.g., the power amplifier response), or poorly understood (e.g., channel models for molecular and underwater communications). In this case, it is unclear how to backpropagate gradients from the receiver to the transmitter [24].