Power Allocation for Cooperative Non-Orthogonal Multiple Access Systems

Cooperative non-orthogonal multiple access (NOMA) has attracted more and more attentions recently, in which NOMA-strong users play as relays to help the data transmission of NOMA-weak users. Different from existing works, we study the problem of power allocation for cooperative NOMA systems with half-duplex relaying mode. From a fairness standpoint, our proposed scheme aims at maximizing the minimum achievable user rate in a paired user group. More specifically, we divide the cooperative NOMA systems into two categories, i.e., fixed relaying scheme and adaptive relaying scheme. Fixed relaying scheme means the transmit power at the relay node, namely PR, is a given fixed constant while adaptive relaying scheme implies that PR$ can adapt to channel conditions according to our strategy. It is shown that the formulated power allocation problem for fixed relaying scheme is quasi-concave while the problem for adaptive relaying scheme is not. Hence, we firstly solve the former problem using a bisection algorithm by transforming it into a sequence of convex feasibility problems. Then, relying on the derived results of fixed relaying scheme, we find that the problem for adaptive relaying scheme can be converted into a univariate function about PR, in which the optimum can be also obtained by a similar bisection procedure. Numerical results reveal that the proposed adaptive relaying scheme always outperforms the proposed fixed relaying scheme. In addition, we also show that the cooperative NOMA systems are especially appropriate for systems under low SNR environments or having significantly different fading coefficients between NOMA users.