[Paper Review] On the Maximum Sum-rate Capacity of Cognitive Multiple Access Channel

Peng Cheng, Guanding Yu+3 more|ArXiv.org|Dec 5, 2006

Wireless Communication Security Techniques3 references3 citations

TL;DR

This paper investigates the maximum sum-rate capacity in a cognitive multiple access channel where multiple cognitive users communicate with a common access point while causing no interference to a primary user. By modeling the system as a Gaussian MAC with dirty paper coding and cooperation, the authors formulate a nonlinear optimization problem for power allocation and propose an iterative Lagrangian multiplier-based algorithm to achieve the optimal sum-rate, with the key result being a closed-form expression for the optimal power ratio in the cooperation term.

ABSTRACT

We consider the communication scenario where multiple cognitive users wish to communicate to the same receiver, in the presence of primary transmission. The cognitive transmitters are assumed to have the side information about the primary transmission. The capacity region of cognitive users is formulated under the constraint that the capacity of primary transmission is not changed as if no cognitive users exist. Moreover, the maximum sum-rate point of the capacity region is characterized, by optimally allocating the power of each cognitive user to transmit its own information.

Motivation & Objective

• To characterize the capacity region of a cognitive multiple access channel where multiple cognitive users transmit to a common AP without degrading primary user performance.
• To address the challenge of maximizing the sum-rate of cognitive users under primary user rate and interference constraints.
• To develop an efficient power allocation strategy that optimizes spectral efficiency while maintaining primary user transmission quality.
• To provide a practical algorithm for achieving the maximum sum-rate in cognitive radio networks with multiple co-channel cognitive users.

Proposed method

• Models the cognitive MAC as a Gaussian multiple access channel with interference from a primary user, incorporating both dirty paper coding and cooperation terms.
• Derives the capacity region as a function of power allocation parameters, particularly the cooperation gain $\gamma_k$ for each cognitive user.
• Formulates the sum-rate maximization as a nonlinear optimization problem constrained by the primary user's rate requirement and interference limits.
• Introduces a Lagrangian dual method to solve the non-convex optimization problem, with an iterative algorithm to compute the optimal $\gamma_k$ values.
• Uses an iterative procedure that dynamically updates the active set $\mathcal{S}$ of users with $\gamma_k < 1$, adjusting $X$ and $\gamma_k$ at each step based on the current state.
• Employs a stepwise search over the Lagrange multiplier $\lambda$, starting from $\lambda = 0$, to converge to the optimal solution satisfying all constraints.

Experimental results

Research questions

• RQ1 What is the achievable capacity region of a cognitive multiple access channel with multiple cognitive users and a primary user?
• RQ2 How can the sum-rate of cognitive users be maximized under the constraint that the primary user's rate is unaffected?
• RQ3 What is the optimal power allocation strategy, including cooperation and dirty paper coding, to achieve the maximum sum-rate?
• RQ4 How can the non-convex optimization problem for sum-rate maximization be solved efficiently in practice?
• RQ5 What is the impact of channel gains and power constraints on the optimal cooperation factor $\gamma_k$?

Key findings

• The capacity region of the cognitive MAC is characterized as a union of regions parameterized by feasible cooperation factors $\boldsymbol{\gamma}$, with the maximum sum-rate point lying on the boundary.
• The optimal sum-rate is achieved when the cooperation factor $\gamma_k$ for each cognitive user is chosen to balance interference cancellation and power efficiency.
• The iterative algorithm converges to the optimal $\gamma_k$ values by dynamically updating the active set $\mathcal{S}$ of users not at the boundary ($\gamma_k < 1$).
• The solution depends on the channel gains $h_k$, $g_k$, and $h_p$, as well as the power constraints $P_k$ and $P_p$, with $\gamma_k$ derived from a Lagrangian dual formulation.
• The algorithm starts from $\lambda = 0$ and increases $\lambda$ in steps, recalculating $X$ and $\gamma_k$ at each iteration until all constraints are satisfied.
• The optimal $\gamma_k$ is given by $\gamma_k = \frac{\lambda \sigma_p^2 X}{(\beta_k^2 - \lambda h_p^2 P_p) g_k \sqrt{P_k}}$ when $\gamma_k < 1$, and set to 1 otherwise, with $\beta_k = h_k / g_k$.