NOMA_JSPA_WSR

A Python 3 implementation of the Joint Subcarrier and Power Allocation algorithms for WSR maximization in NOMA described in the following paper: L. Salaün, M. Coupechoux, and C. S. Chen, "Joint Subcarrier and Power Allocation in NOMA: Optimal and Approximate Algorithms." IEEE Transactions on Signal Processing, vol. 68, pp.2215-2230, 2020.

© 2016 - 2020 Nokia
Licensed under Creative Commons Attribution Non Commercial 4.0 International
SPDX-License-Identifier: CC-BY-NC-4.0

Getting started

We first start by defining the following system parameters:

• K (integer) : number of users.
• L (integer) : number of subcarriers.
• Multiplex (integer) : number of users per subcarrier.
• Radius (float) : radius of the cell in meters.
• rmin (float) : min distance between a user and the BS.
• G (array of size (K,L)) : channel gains for each user on each subcarrier. This can be generated randomly following the above paper's propagation model using G = generate_gains.generateGains(K,L,Radius,rmin).
• B (float) : total bandwidth.
• W (array of size L) : array of each subcarrier's bandwidth, usually: W = np.ones(L)*B/L.
• N (array of size KL) : array of noises for each user on each subcarrier. For example: N = 10**((-174-30)/10)*B/L*np.ones(K*L) corresponds to -174 dBm/Hz.
• N_G (array of size (L,K)) : noise over channel gains array, obtained by N_G = ca_jspa.computeN_G(G,N).
• pi and pi_inv (array of size (L,K)) : decoding order and its inverse function obtained by pi, pi_inv = ca_jspa.computePi(G,N).
• w (array of size K) : one weight for each user, which is used to define the weight sum-rate (WSR) objective function.
• Pmax (float) : the total cellular power budget available for DL transmission.
• PmaxN (array of size L) : power budget for each subcarrier (Note: this parameter is not used by algorithms Grad_JSPA, SpeedUp_Grad_JSPA and eqPow_JSPA).

The Joint Subcarrier and Power Allocation (JSPA) algorithms are implemented in "channel_allocation_JSPA.py". They all consider weighted sum-rate (WSR) as objective function. Below is a summary of the main algorithms:

• Opt-JSPA:
  • Can be called using opt_JSPA(K,L,Multiplex,Pmax,PmaxN,N_G,pi,pi_inv,w,W,delta).
  • It finds the optimal WSR assuming the power allocation is discretized with precision delta. That is, the allocated powers can only take value of the form l*delta, where l is in {0,1,...,floor(Pmax/delta)}.
  • Its computational complexity is in O((Pmax/delta)^2), disregarding K and L.
• epsilon-JSPA:
  • Can be called using epsilon_JSPA(K,L,Multiplex,Pmax,PmaxN,N_G,pi,pi_inv,w,W,epsilon).
  • It computes an approximate solution that achieves at least (1-epsilon) times the optimal WSR. As a consequence, epsilon should be set between 0 and 1 excluded.
  • It is a FPTAS with computational complexity in O((1/epsilon)^2), disregarding K and L.
• Grad-JSPA:
  • Can be called using SpeedUp_Grad_JSPA(K,L,Multiplex,Pmax,N_G,pi,pi_inv,w,W,delta,rounding_step=None).
  • It is a heuristic based on the projected gradient method, where delta represents the error tolerance at termination, and rounding_step is the final power allocation rounding/discretization precision. By default rounding_step = None means that no rounding is performed on the final power allocation.
  • Grad_JSPA(K,L,Multiplex,Pmax,N_G,pi,pi_inv,w,W,delta,rounding_step=None) gives the same result but with larger running time since it uses the basic SCUS instead of SpeedUpSCUS as basic building block. Hence, SpeedUp_Grad_JSPA is preferred.
• eqPow-JSPA:
  • Can be called using eqPow_JSPA(K,L,Multiplex,Pmax,N_G,pi,pi_inv,w,W).
  • It is a simple heuristic that allocates equal power budget on each subcarrier, then it solves SCUS once for each subcarrier.

In summary, when looking for an optimal solution, Opt-JSPA should be used. In this case, delta is chosen according to the transmit power precision required by the system (for example 10 mW for a total power budget of 1W). epsilon-JSPA provides an approximate solution. It has lower complexity than Opt-JSPA as long as epsilon is not too small. Otherwise, Opt-JSPA should be used instead. Grad-JSPA and eqPow-JSPA can be used to obtain low complexity solutions with good performance in average (without any performance guarantee). These JSPA algorithms are shown in file "example_JSPA.py".

Some examples of the single-carrier algorithms SCPC and SCUS can be found in "example_SCPC.py" and "example_SCUS.py". These two algorithms are mainly used as building blocks inside the JSPA algorithms.