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Randomized Power Transmission with Optimized Level Selection Probabilities in Uncoordinated Uplink NOMA

Noura Sellami, Mohamed Siala

TL;DR

The paper tackles uncoordinated uplink NOMA by optimizing the probabilities of selecting predetermined power levels to minimize the average BLEP $\overline{P}_E$. It derives a quadratic programming formulation when the BS detector handles at most two colliding packets ($K\le 1$) and extends to an iterative approach for larger collisions ($K\ge 2$), all applicable to any multiuser detection algorithm. The approach leverages a Poisson activity model and truncated BLEP $\overline{P}_{E_T}$ to compute the objective, with explicit case-study and simulations showing substantial BLEP gains over a uniform power-level distribution, especially for larger $Q$ and higher $\gamma_Q$. The results demonstrate practical benefits for uncoordinated uplink NOMA and provide a flexible framework compatible with various detectors and power-level sets.

Abstract

We consider uncoordinated random uplink non-orthogonal multiple access (NOMA) systems using a set of predetermined power levels. We propose to optimize the probabilities of selection of power levels in order to minimize performance metrics as block error probability (BLEP) or bit error probability (BEP). When the multiuser detection algorithm at the BS treats at most two colliding users' packets, our optimization problem is a quadratic programming problem. For more colliding users' packets, we solve the problem iteratively. Our solution is original because it applies to any multiuser detection algorithm and any set of power levels.

Randomized Power Transmission with Optimized Level Selection Probabilities in Uncoordinated Uplink NOMA

TL;DR

The paper tackles uncoordinated uplink NOMA by optimizing the probabilities of selecting predetermined power levels to minimize the average BLEP . It derives a quadratic programming formulation when the BS detector handles at most two colliding packets () and extends to an iterative approach for larger collisions (), all applicable to any multiuser detection algorithm. The approach leverages a Poisson activity model and truncated BLEP to compute the objective, with explicit case-study and simulations showing substantial BLEP gains over a uniform power-level distribution, especially for larger and higher . The results demonstrate practical benefits for uncoordinated uplink NOMA and provide a flexible framework compatible with various detectors and power-level sets.

Abstract

We consider uncoordinated random uplink non-orthogonal multiple access (NOMA) systems using a set of predetermined power levels. We propose to optimize the probabilities of selection of power levels in order to minimize performance metrics as block error probability (BLEP) or bit error probability (BEP). When the multiuser detection algorithm at the BS treats at most two colliding users' packets, our optimization problem is a quadratic programming problem. For more colliding users' packets, we solve the problem iteratively. Our solution is original because it applies to any multiuser detection algorithm and any set of power levels.

Paper Structure

This paper contains 8 sections, 15 equations, 7 figures.

Table of Contents

  1. Introduction
  2. System model
  3. Optimization problem
  4. Collision of at most two users' packets ($K \leq 1$)
  5. Collision of more than three users' packets ($K \geq 2$)
  6. Case study
  7. Simulation results
  8. Conclusion

Figures (7)

  • Figure 1: Received constellation and decision boundaries. (a) $\gamma_{i_0}>\gamma_{i_1}$. (b) $\gamma_{i_0}<\gamma_{i_1}$. (c) $\gamma_{i_0}=\gamma_{i_1}$.
  • Figure 2: BLEP versus $Q$ for BPSK modulation, different values of $\gamma_Q$ and $K=1$, when the optimized distribution is used (solid curves) and when the uniform distribution is used (dashed curves)
  • Figure 3: BLEP versus $Q$ for BPSK modulation, different values of $\gamma_Q$ and $K=2$, when the optimized distribution is used (solid curves) and when the uniform distribution is used (dashed curves)
  • Figure 4: Distribution of the received SNR at the BS for BPSK modulation, $K=1$, $\gamma_{Q,dB}=33dB$ and different values of $Q$: the optimized distribution (solid curves) and uniform distribution (dashed curves)
  • Figure 5: Throughput versus $Q$ for BPSK modulation, different values of $\gamma_Q$ when the optimized distribution is used for $K=1$ (solid curves) and $K=2$ (dashed curves)
  • ...and 2 more figures