By. Hina Tabassum

The next generation of wireless networks is anticipated to be more complex and heterogeneous due to higher transmission frequencies, massive antenna arrays, ultra-dense deployments, mobility of transceivers, and static/dynamic link blockages. These features lead to faster variations in the propagation channel. Subsequently, the wireless channel coherence time (the time during which the transmission channel remains stable) is reducing which necessitates faster and proactive network resource management solutions. To date, communication system designers were mainly relying on conventional optimization algorithms for radio resource management (RRM). However, the traditional network optimization and RRM solutions are generally not applicable as they are not scalable and are not fast enough to compensate the short channel coherence time. Deep learning enables overcome those challenges by training deep neural networks (DNNs) in an offline manner. Once trained, the time complexity of obtaining network resource allocation variables from the networks become significantly lower than the traditional optimization-based approaches.

As such, in our research lab, we recently explored the potential of data-driven unsupervised learning algorithms for constrained convex and non-convex network optimization and RRM problems. It is noteworthy that while DNNs can minimize the time complexity, satisfying sophisticated convex/non-convex constraints is a fundamental challenge regardless of the supervised or unsupervised training method.

In the sequel, we developed two novel solutions with applications to classical wireless power control problem in a multi-user interference channel with non-convex quality of service (QoS) and power budget constraints. The first is called Deep Implicit Projection Network (DIPNet), and the second is called Deep Explicit Projection Network (DEPNet). The former requires convex constraints; whereas, the latter does not.

  • In DIPNet, we define the projection function implicitly using the concept of differentiable convex optimization (DCO) layers which require reformulating the constraints of the original problem as convex constraints and choosing a convex objective function for this layer. DCO layer, a type of implicit layer in DNNs, to implicitly define a projection function. The projection function projects the neural network’s output to the feasible set defined by the QoS and power budget constraints. Thus, the DNN’s output always satisfies the constraints.
  • DEPNet considers differentiable and explicitly-defined projection function that projects the output of DNN to the feasible set of the problem with reduced computational complexity. It uses a differentiable iterative process to realize the projection function and moves the output of the neural network closer to the feasible set. Each iteration uses a process, called correction process, which corrects the previous output towards lesser violation of the constraints. This approach uses soft-loss during training and shows faster performance relative to the first approach at the expense of the lack of the provable feasibility of the results.

The aforementioned research work has been recently extended to demonstrate its applicability in joint beamforming and phase-shift optimization in reconfigurable intelligent surface (RIS)- enabled wireless networks. We have proposed an efficient projection function that searches inside the feasible space and achieves better performance.

The developed solutions are general to handle convex and non-convex constraints in any optimization problem irrespective of the domain and are agnostic to the choice of neural network architectures.

References:

[1] M. Alizadeh and H. Tabassum, “Power Control with QoS Guarantees: A Differentiable Projection-based Unsupervised Learning Framework,” IEEE Transactions on Communications (IEEE TCOM), 2023.

[2] M. Alizadeh, X. Mootoo, O. Waqar, and H. Tabassum, “QoS-Aware Deep Unsupervised Learning for STAR-RIS Assisted Networks: A Novel Differentiable Projection Framework,” in IEEE Wireless Communications Letters (IEEE WCL), 2024