Spectrum resources are the precious and limited natural resources. In order to improve the utilization of spectrum resources and maximize the network throughput, this paper studies the resource allocation of the downlink cognitive radio network with non-orthogonal multiple access (CRN-NOMA). NOMA, as the key technology of the fifth-generation communication (5G), can effectively increase the capacity of 5G networks. The optimization problem proposed in this paper aims to maximize the number of secondary users (SUs) accessing the system and the total throughput in the CRN-NOMA. Under the constraints of total power, minimum rate, interference and SINR, CRN-NOMA throughput is maximized by allocating optimal transmission power. First, for the situation of multiple sub-users, an adaptive optimization method is proposed to reduce the complexity of the optimization solution. Secondly, for the optimization problem of nonlinear programming, a maximization throughput optimization algorithm based on Chebyshev and convex (MTCC) for CRN-NOMA is proposed, which converts multi-objective optimization problem into single-objective optimization problem to solve. At the same time, the convergence and time complexity of the algorithm are verified. Theoretical analysis and simulation results show that the algorithm can effectively improve the system throughput. In terms of interference and throughput, the performance of the sub-optimal solution is better than that of orthogonal-frequency-division-multiple-access (OFDMA). This paper provides important insights for the research and application of NOMA in future communications.

The secondary users (SUs) of the cognitive radio network (CRN) can have an opportunity to access the licensed spectrum of the primary user (PU). Therefore, spectrum utilization can be improved by sharing spectrum between SUs and PU. At present, the researches about CRN mainly focus on the network resources allocation. However, the flexibility of radio spectrum access brings new challenges to CRN.

How to use the limited spectrum resources to provide higher transmission rates for more users has always been a focus and research issue in the wireless communication field. With the fifth-generation mobile communication network (5G) technology becoming more and more attractive, 5G has been widely used in a large number of applications [

CRN based on NOMA technology is called CRN-NOMA. When more SUs access the CRN-NOMA, the spectrum efficiency and total throughput of the system can be effectively improved. In view of the power domain multiplexing characteristics of NOMA, the SUs of CRN-NOMA multiplex the sub-channel of the PU in the manner of NOMA. On the one hand, the transmitter performs power allocation according to the channel gains of different SUs. On the other hand, the receiver uses successive interference cancellation (SIC) technology to correctly demodulate through different power values in order to distinguish the target signal from the interference signal [

At present, there are many research works related to NOMA in wireless transmission. It can be seen from these research studies that SIC and power multiplexing are the key technologies of NOMA. Among them, power multiplexing technology is a research hotspot of scholars. Unlike ordinary power control, the NOMA power multiplexing technology is used by the base station (BS) to perform power allocation through related algorithms, and to achieve certain performance with limited resources.

Wang et al. [

In view of the shortcomings of fixed transmit power, researchers have initiated studies on CRN-NOMA [

In order to expand the transmission distance, some scholars have studied the relay CRN-NOMA. Chu et al. [

Form the previous analysis, it can be seen that the current research works of CRN-NOMA mainly focus on the outage probability, traversal capacity, user fairness and resource allocation. The communication scenarios of tow SUs are mainly studied. However, with the increasing complexity of the network structure, the optimization of multi-user CRN-NOMA throughput is also an interesting research direction. This paper investigates the optimization problem in the multi-user CRN-NOMA scenario, namely the number of SUs accessing the system and the total system throughput. Under multiple constraints, CRN-NOMA throughput is improved by allocating optimal transmission power of SUs.

This paper mainly studies the problem of CRN-NOMA power allocation optimization, i.e., SUs accessing number and throughput optimization. The main contributions of this paper are as follows:

First, at the transmitting end, power allocation is performed according to the channel conditions of the SUs. In order to meet the communication requirements of multi-user scenarios, the superimposed coding technology is used to send signals to multiple SUs at the same time. The transmitter ensures user performance by adjusting the power distribution coefficient.

Secondly, different SUs have different signal strengths at the receiving end. In accordance with the order of signal strength, SIC technology is used for signal demodulation. Signals with high strength are demodulated first, and this signal component is subtracted. Then the weak signals are demodulated in turn, and finally the useful signal is recovered.

Then, in order to avoid the high complexity of the algorithm, an adaptive search algorithm is used to solve the maximum number of connected SUs.

Finally, Chebyshev is used to transform the multi-objective optimization problem into single-objective optimization problem. A maximization throughput algorithm based on Chebyshev and convex optimization (MTCC) is proposed, which has the characteristics of low complexity and fast convergence.

The remainder of this paper is organized as follows. The network and system model are introduced in Section 2. In Section 3, the power allocation study for maximum SUs access number and throughput in a CRN-NOMA scenario is formulated. Based on Chebyshev and convex optimization (MTCC) are designed in Section 4. Numerical and simulation results are presented in Section 5. Finally, Section 6 concludes this paper.

As shown in _{PBS}

We use _{i}_{i}_{PBS, PU}, _{PBS, SBS} and _{SBS, SUi} respectively, where

Since CRN-NOMA adopts the underlay spectrum sharing model, the access _{i}_{i}_{SUi} for signal _{SBS, SUi} of remote user (_{i}_{SUi −1} for signal _{SBS, SUi −1} of near user (_{i −1}).

We assume that the channel gains of the communication links of the SUs are sorted in descending order, and then the signal power of these SUs is arranged in ascending order. The specific assumption is as follows, the order of channel gain from SBS to its _{i}

Each level of the SIC detector only detects one signal, so _{SBS, SUN} is the strongest, _{SBS, SUN} is judged first, and _{SBS, SUN} is output. Then the signal estimation of _{SBS, SUN} is restored, and _{SBS, SUN} is subtracted from the received signal. The estimated value is _{SBS, SU1}, _{SBS, SU1} is used as the next level to complete all user operations.

The NOMA system model is shown in _{PU}

where _{PBS}_{PBS, PU} is the transmission data signal of PBS. _{PBS, PU} is additive white Gaussian noise with mean value of zero and variance of

We can write the received signal at SBS as follows:

where _{PBS, SBS} is the transmission data signal of PBS to SBS. _{PBS, SBS} is additive white Gaussian noise with mean value of zero and variance of

The SBS broadcasts the NOMA signal to _{i}

where _{SBS}_{i}_{i}

We can substitute the

where _{SBS}_{PU}_{SUj} are the transmission power of SBS, PU and _{j}_{SBS, SUi}, _{PU, SUi}, _{SUj, SUi} is the transmission data signal of SBS to _{i}_{i}_{j}_{i}_{SBS, SUi} also is additive white Gaussian noise with mean value of zero and variance of

According to the characteristics of NOMA, SU with poor channel gain will first uses SIC technology to eliminate other SUs signals with better channel conditions, and then decode their own signals. According to

According to Shannon theorem, we can give the transmission rate (bits/s/Hz) of PU and _{i}

According to the characteristics of CRN, in order to ensure the normal communication between PU and SUs, some condition constraints (e.g., power constraints, minimum SINR constraints, interference temperature constraints and outage probability constraints, etc.) need to be met. In this paper, the first three constraints will be considered. First, the power of PU and SUs cannot exceed the maximum power

Similarly, in order to ensure the QoS of PU and SUs, the SINR constraints must be met.

where

Because of the underlay CRN-NOMA studied in this paper, the interference of SUs to PU must satisfy certain conditions, that is, the interference temperature of PU cannot be exceeded. We can use the following expression to express this relationship.

where _{SUi} is the power of the _{SUi, PU} is the channel gains of _{i}

This research investigates the optimal power control problems between PU and SUs in each time slot, and studies the accessed number maximization problem and the system throughput maximization problem with some constraints (i.e., power constraints, minimum SINR constraints and interference temperature constraints).

First, our optimization goal is to allocate power among SUs to maximize the total number

where _{SUi} represents the power allocation factor of the _{i}_{SUi} is the signal power vector of the

Then, the second optimization problem studied in this paper is to maximize the throughput of the secondary network under power allocation condition. We mark this optimization problem as

It can be seen from

Since our paper considers the CRN-NOMA downlink communication scenario, the power of _{i}

According to _{SBS}

According to _{1}, _{1} with the best channel status until the end of the _{N}

Then we can calculate the range of _{i}

It is assumed that each SU communicates with the minimum rate limit. Therefore, the power allocation process can start from _{1} with the best channel and end with _{N}_{N}

We can put it another way, to maximize the total throughput of the system in problem

Our solution is to first prove that there is a unique solution to the optimization problem, and then propose a low-time complexity algorithm to solve the throughput maximization problem. We propose a throughput maximization solution based on the Chebyshev algorithm, which transforms the convex multi-objective optimization problem into a single-objective optimization problem.

_{SUi} is the throughput of _{i}_{n}_{i}_{n}

Channel gain is a random variable, and its cumulative distribution function (CDF) can be written as follows:

where _{SBS, SUi} is the distance from SBS to _{i}

According to the reference [

where

It can be seen from

According to the theory of dual decomposition, we relax the constraints and construct the Lagrange function:

While

The dual function of

The dual problem of

In order to obtain the optimal power for each _{i}

We can get the optimal transmission power

We propose a maximum throughput algorithm for CRN-NOMA based on Chebyshev and Convex optimization, which specific steps are shown in

1) Initialization: _{SBS}_{SBS, SUi}, _{PBS, SUi};

2) Given the _{SBS}

3) Given the _{SUi}, using the Chebyshev and convex algorithm, maximization throughput strategy _{SUi} is obtained;

4)

5) Repeat Steps 2) to 4) until

6) Output:

Watkins proved the convergence of the Chebyshev algorithm under certain conditions [

Computational complexity issues are significant in all research aspects of CRN-NOMA. Reference [_{SUi} and for each state. Therefore, its computational complexity is

In this section, numerical simulations are used to evaluate the performance of the proposed algorithm. The simulation assumes that the network coverage is 150 and 150 m, where PBS, SBS, PU and SUs are randomly distributed in the network. The maximum distance from SU receiver to SBS is 50 m, and the fading follows Rayleigh distribution. The system simulation parameters are set as shown in

Parameters | Value | Parameters | Value |
---|---|---|---|

Channel | Rayleigh | Noise power |
−120 dBm/Hz |

Spectrum bandwidth |
5 MHz | Interference temperature |
−50 dBm |

Distance to SBS _{SBS, SUi} |
[1:1:50] m | Path-loss exponent |
3 |

BS maximum power |
7 dBm | PUSINR threshold |
2 dB |

Number of PU | 1 | _{i} |
0.5 bB |

Number of SUs |
[1:1:20] | Chebyshev approximation term |
10 |

This part only simulates the downlink communication scenario of CRN-NOMA. Consider the mutual interference between PU and SUs, SUs and SUs. If the interference caused by SUs to PU causes the SINR of the PU to always be higher than its normal communication threshold, the SUs will not affect the normal communication of PU. The numerical data for the specific experiment is composed as follows.

As shown in _{4} has the farthest distance, followed by _{3}. In communication, if the distance increases, the bit error rate (BER) will increase. When the SINR is less than 15 dB, for four SUs with the same SINR value, a SU with a larger power allocation factor has a higher BER. Therefore, it can be seen that _{1} has the lowest BER, followed by _{2}, _{3} and _{4}.

In the following, in order to evaluate the effectiveness of the proposed algorithm, we compare the algorithm with other power allocation algorithms. The legends “Optimal-NOMA,” “FTPA-NOMA” and “Optimal-OFDMA” respectively represent the power allocation scheme that proposed in this paper in the NOMA scenario, the fractional transmit power allocation (FTPA) scheme in the NOMA scenario and the power allocation scheme in the OFDMA scenario. The FTPA algorithm allocates power according to the size of the user channel gain and the pre-defined attenuation factor of the system [

In

In summary, in the process of studying the optimal resources allocation of CRN-NOAM, we propose to use an adaptive method and a method of transforming Chebyshev inequality to convex optimization (MTCC) to solve two optimization problems, i.e., maximizing the number of SUs accessing SBS and maximizing system throughput. The objective of optimization is to maximize the number of access users and system throughput, and is constrained by QoS of PU and SUs, power control, interference constraints and power allocation factors. The Lagrangian duality method is used to transform the non-convex optimization problem into a convex optimization problem. Finally, the optimal heuristic algorithm is used to obtain the optimal solution. The algorithm MTCC proposed in this paper helps to improve the system throughput and spectrum utilization efficiency, and provides a reasonable resource allocation plan. Through experimental simulation, the effect is better than OMA’s power allocation scheme.

The authors would like to thank the anonymous reviewers for their selfless reviews and valuable comments, which have improved the quality of our original manuscript.