# Non-orthogonal multiple access with joint maximum likelihood detection in heterogeneous network

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## Abstract

As one of the key technologies in the fifth-generation mobile communication system, non-orthogonal multiple access (NOMA) has been investigated. In NOMA, multiple terminals are assigned the same frequency resources by a scheduler on the basis of the difference in propagation losses between a base station and user terminals. Each terminal cancels the signals for the other terminals and extracts its desired signal. On the other hand, the application of joint maximum likelihood (ML) detection to overloaded signals has also been investigated, and joint ML detection can be applied to a NOMA downlink. In this paper, the effect of joint ML detection in a heterogeneous NOMA network is presented. The numerical results obtained through system-level simulation show that joint ML detection in a heterogeneous NOMA downlink can effectively offload mobile traffic from a macro base station to a pico base station. It is shown that a heterogeneous NOMA network with joint ML detection improves the throughput performance by 0.2 bit/user/subcarrier as compared to that without joint ML detection at a cumulative probability of 0.5. The system throughput is also increased about twofold with joint ML detection.

## Keywords

Heterogeneous network Proportional fairness scheduling Joint ML detection## Abbreviations

- AWGN
Additive white Gaussian noise

- HetNet
Heterogeneous network

- LTE
Long Term Evolution

- MBS
Macro base station

- MU
Macro user

- MIMO
Multiple-input multiple-output

- ML
Maximum likelihood

- NOMA
Non-orthogonal multiple access

- QAM
Quadrature amplitude shift keying

- QPSK
Quadrature phase shift keying

- PBS
Pico base station

- PU
Pico user

- PF
Proportional fairness

- RMS
Root mean square

- SIC
Successive interference cancelation

- SINR
Signal-to-interference-plus-noise ratio

## 1 Introduction

The amount of mobile traffic has increased explosively in recent years owing to the rise in the penetration rate of mobile devices such as smart phones. It is expected to increase 1000-fold from 2010 to 2020 [1]. To accommodate such a large amount of mobile traffic, the concept of the fifth-generation mobile communication system (5G) has been discussed.

As one of the key technologies in 5G, non-orthogonal multiple access (NOMA) has been proposed and investigated as a mean to improve the spectrum efficiency of the system [2, 3, 4, 5, 6, 7]. In the downlink of the NOMA scheme, multiple user terminals are assigned the same frequency resources. These user terminals are located at different positions relative to a base station, and their propagation losses are different. The base station transmits signals to these user terminals with different transmission powers. The receiver in the user terminal that is closer to the base station eliminates the signals for the other user terminals by interference cancelation and extracts the desired signal. Under practical modulation and coding parameters that enable limited decoding and interference cancelation capability, the powers of the received signals must be sufficiently different to demodulate and decode the undesired signals through interference cancelation. Otherwise, the residual interference caused by unreliable replica symbols will deteriorate the demodulation performance of the desired signal [8]. The improvement in throughput by the NOMA scheme is limited owing to the residual interference even though the number of terminals assigned the same resource is set to more than two [9].

On the other hand, in the LTE-Advanced system, a heterogeneous network (HetNet) has been specified in the standard [10, 11, 12]. In HetNets, small cells called pico cells are placed within a macro cell, and each user terminal is connected to a nearby pico cell to prevent traffic congestion in a macro cell network. However, the interference owing to the signal from the macro base station (MBS) limits the traffic offloading capability of HetNets. The transmission power of the MBS is much larger than that of the pico base station (PBS), and the signal from the PBS must be protected [13, 14].

Some recent studies have treated this problem with NOMA schemes in the downlink [15, 16, 17]. However, not many studies have taken demodulation schemes into account. Codeword-level successive interference cancelation (SIC) requires turbo decoding and replica signal generation. These processes require coding parameters as well as modulation parameters of the signals for the other users. They also cause a demodulation delay that is not acceptable in some applications. Resource block assignment among NOMA users should coincide to reduce the complexity of SIC. If the desired signal with a smaller signal power overlaps with multiple undesired signals, a receiver has to decode all these interference signals for the generation of SIC replicas.

If the number of antenna elements implemented in a user terminal is more than the total number of the desired and interference signals, it is possible to separate the desired signal and the other interfering signals by a normal multiple-input multiple-output (MIMO) detection process. In this case, simple linear detection schemes such as a zero-forcing detection scheme or a minimum mean-square-error detection scheme can be applied. However, owing to the limitation of its form factor, the number of receive antennas may be less than the number of received signal streams. This is an “overloaded" situation, and a nonlinear detection scheme must be applied in the receiver. The joint detection of multiple signal streams in the receiver is a solution to this limitation although joint detection increases the demodulation complexity [18]. Joint detection only requires the channel responses and modulation orders of the interfering signals. In [19], the effect of joint detection in terminals both near and far from a base station located at the center of a cell was investigated. In this case, joint detection works effectively in cell site terminals. In a heterogeneous network, joint detection works effectively in the cell site terminals of a pico cell as they suffer from large interference from a MBS.

Thus, in this paper, the application of joint maximum likelihood (ML) detection to a heterogeneous NOMA network is investigated. The numerical results obtained through system-level simulation show that joint ML detection in a NOMA downlink alleviates the effect of the interference and can offload mobile traffic from the MBS to the PBS.

This manuscript is organized as follows. Section 2 presents the application of the joint ML detection scheme in a heterogeneous NOMA network. The numerical results of the proposed system obtained through system-level simulation are presented in Section 3. Finally, Section 4 gives our conclusions.

## 2 System model

### 2.1 Signal model

Here, it is assumed that a macro user (MU) receives the signal from the MBS, and a pico user (PU) receives the signal from the PBS. User assignment is carried out in each resource block, allowing the same user to be a MU and a PU in different resource blocks. It is also assumed that the PBS is under the control of the MBS in terms of the user assignment, and NOMA between a PU and a MU is assumed.

*U*

_{m}is an index for the MU, and

*U*

_{p}is an index for the PU. It is then assumed that \(x^{l}_{\text {MU}_{m}}(k_{m})\) is the transmitted symbol on the

*l*th subcarrier for the MU from the MBS, \(x^{l}_{\text {PU}_{p}}(k_{p})\) is the transmitted symbol on the

*l*th subcarrier for the PU from the PBS, and the numbers of constellation points in one symbol are

*N*

_{m}(0≤

*k*

_{m}≤

*N*

_{m}−1) and

*N*

_{p}(0≤

*k*

_{p}≤

*N*

_{p}−1) in the signals for the MU and PU, respectively. The channel responses and their phase rotation terms from the MBS to the MU, from the MBS to the PU, from the PBS to the MU, and from the PBS to the PU on the

*l*th subcarrier are defined as \(h^{l}_{\text {MU}_{m}}\) and \(\exp \left (j\theta ^{l}_{\text {MU}_{m}}\right)\), \(h^{l}_{\text {MU}_{p}}\) and \(\exp \left (j\theta ^{l}_{\text {MU}_{p}}\right)\), \(h^{l}_{\text {PU}_{m}}\) and \(\exp \left (j\theta ^{l}_{\text {PU}_{m}}\right)\), and \(h^{l}_{\text {PU}_{p}}\) and \(\exp \left (j\theta ^{l}_{\text {PU}_{p}}\right)\), respectively, and they are given as follows:

*U*

_{m}th MU is then given as:

*σ*

^{2}. On the other hand, the signal received by the

*U*

_{p}th PU is:

where \(z^{l}_{p}\) is also AWGN with a mean of 0 and a variance of *σ*^{2}.

### 2.2 Throughput of NOMA with joint ML detection in HetNet

In this study, as explained in detail in the Appendix, the constellation constraint capacity is calculated as the throughput of the system [20, 21, 22]. Furthermore, it is assumed that \(\alpha ^{l}_{M}, N_{m},\) and *N*_{p} are determined in each resource block.

*T*

_{m}(

*U*

_{p},

*l*) and

*T*

_{m}(

*U*

_{p},

*l*) are the instantaneous throughputs of the

*U*

_{m}th MU and

*U*

_{p}th PU on the

*l*th subcarrier, respectively. The throughput of the MU is calculated as Eq. (11) and that of the PU is calculated as Eq. (12).

### 2.3 Proportional fairness scheduling

*u*is the user index; {

*Ω*

_{m}} and {

*Ω*

_{p}} are the groups of subcarriers assigned to the

*u*th user as the MU and the PU, respectively;

*t*is the time index; and

*t*

_{c}is the period of the moving average [23]. From the above equation, the PF metric is given as:

*Ω*

_{b}} is the set of subcarrier indexes in the

*b*th resource block. Through this user assignment process, the pair of users, the modulation parameters, and the transmission power from the base station that maximizes Eq. (14) are obtained. The user throughput for the

*u*th user is then given as:

*u*th user is calculated as:

## 3 Method

*μ*s, the maximum Doppler shift,

*f*

_{D}, is set to 5.55 Hz, and a six-path exponential delay profile fading channel model is assumed. There are 12 subcarriers in 1 resource block, 1 subband consists of 24 resource blocks, 1 resource block occupies 180 kHz, and the frequency bandwidth of the channel is 4.32 MHz. The spectrum density of the noise in the receiver is assumed to be − 174 dBm/Hz. In the calculation of the SINR, the interference from the 18 surrounding MBSs and that from the pico cells located in the adjacent sectors to the sector of concern are taken into account. When the PBS is located at the cell edge, it is assumed that a directional antenna is used and no intercell interference from the PBSs in the adjacent cells occurs [24].

Simulation conditions

Scheduling algorithm | PF scheduling |
---|---|

Modulation scheme | QPSK, 16QAM, 64QAM, 256QAM |

Cell layout | 19-hexagonal-cell site |

Inter-site distance | 500 m |

Minimum distance (MBS - user) | 35 m |

Minimum distance (PBS - user) | 10 m |

Number of user terminals per sector | 5, 10, 20 |

Distribution of user terminals | Uniform |

MBS height | 35 m |

PBS height | 10 m |

User height | 1.5 m |

MBS maximum transmission power | 43 dBm |

PBS total transmission power | 30 dBm |

Distance-dependent path loss (MBS) | 128.1 + 37.6log10( |

Distance-dependent path loss (PBS) | 140.7 + 36.7log10( |

Shadowing standard deviation (MBS) | 5 dB |

Shadowing standard deviation (PBS) | 7 dB |

Shadowing correlation | 0.5 |

Channel model | Six-path Rayleigh |

System bandwidth | 4.32 MHz |

Number of resource blocks | 24 |

Resource block bandwidth | 180 kHz |

Receiver noise density | − 174 dBm/Hz |

Time interval | 100 |

User drops | ≥ 50 |

Trial per user drops | 30 |

Number of symbols per trial | 100 |

The average throughput is calculated over 100 time slots for each user drop. The number of user drops is more than 50 for each condition, and the number of trials per user drop is 30. The number of symbols transmitted per trial is 100, and the last 80 symbols are used for throughput evaluation.

## 4 Result and discussion

### 4.1 Offloading capability

### 4.2 Pico base station location

This is because the interference from the MBS is alleviated owing to the joint ML detection in the user terminals. If the PBS is located close to the MBS, it cannot effectively cover the user terminals at the cell edge. If it is too close to the cell edge, the PBS suffers from intercell interference. Thus, the maximum throughput is realized when the PBS is located at a distance of two thirds of the cell radius. When the PBS is located at the cell edge, its coverage area reduces to one third owing to the use of the directional antenna. Thus, without joint ML detection, the throughput and the user fairness are less than those at a distance of five sixths of the cell radius even though no intercell interference from the PBSs in the adjacent cells is assumed. On the other hand, with joint ML detection, the user fairness is greater than that at a distance of five sixths of the cell radius although the throughput is slightly lower. This is because joint ML detection enlarges the coverage area of the PBS, and the PBS realizes better connections to the cell edge users that suffer from intercell interference from the MBSs in the adjacent cells.

## 5 Conclusions

In this study, a joint ML detection scheme for the demodulation of overloaded signals has been applied to the heterogeneous NOMA network. The joint ML detection effectively alleviates the effect of the interference between the signals from the MBS and PBS. The numerical results obtained through system-level simulation have shown that joint ML detection in the NOMA downlink effectively offloads mobile traffic from the MBS to the PBS. As a result, user fairness improves, and the system throughput increases about twofold. The maximum system throughput is achieved when the PBS is at a distance of two thirds of the cell radius from the base station if joint ML detection is applied.

## 6 Appendix A: Derivation of throughput

### 6.1 A.1 Throughput with joint ML detection

*l*th subcarrier is given as:

*y*

^{l}is the received signal, \(\left |h^{l}_{d}\right | \exp \left (j \theta ^{l}_{d}\right)\) is the channel response between a receiver and a base station that transmits a desired signal, \(|h^{l}_{i}|\) is the channel response between the receiver and a base station that causes interference, \( \exp (j \theta ^{l}_{d})\) is the relative phase difference between \(h^{l}_{d}\) and \(h^{l}_{i}\), \(x^{l}_{d}(k_{d})\) is the symbol with the

*k*

_{d}th constellation point of the desired signal, \(x^{l}_{i}(k_{i})\) is the symbol with the

*k*

_{i}th constellation point of the interference signal, and

*z*

^{l}is the AWGN. The CCC for the joint ML detection of

*x*

_{d}(

*k*

_{d}) and

*x*

_{i}(

*k*

_{i}) is calculated in the same way as in [22]. When \(x^{l}_{d}(k_{d})\) and \(x^{l}_{i}(k_{i})\) are received, the distribution of the received signal is equal to that of the AWGN,

*z*

^{l}, and it is given as:

*σ*

^{2}is the variance of the AWGN. Joint ML detection calculates a likelihood with the knowledge of channel responses and modulation orders for both the desired and interference signals as follows. The likelihood for the

*k*

_{d}th constellation point of the desired signal is given by:

*N*

_{i}is the number of constellation points in the interference signal. The probability density function of

*y*

^{l}is then given by:

where *N*_{d} is the number of constellation points in the desired signal.

*y*is given as:

The first term of Eq. (22) is the amount of entropy for the *N*_{d}·*N*_{i} constellation points, and the second term is the average ambiguity of the received signal caused by the noise when joint ML detection is employed.

Equation (24) becomes Eq. (11) by setting *N*_{d}=*N*_{m}, *N*_{i}=*N*_{p}, *k*_{d}=*k*_{m}, *k*_{i}=*k*_{p}, *i*_{d}=*i*_{m}, *i*_{i}=*i*_{p}, \(|h^{l}_{d}|=\alpha ^{l}_{M}|h^{l}_{\text {MU}_{m}}|\), \(|h^{l}_{i}|=|h^{l}_{\text {PU}_{m}}|\), \(\theta ^{l}_{d} = \theta ^{l}_{U_{m}}\), \(z^{l}=z_{m}^{l}\), \(x^{l}_{d}(k^{l}_{d})=x^{l}_{\text {MU}_{m}}(k_{m})\), and \(x^{l}_{i}(k^{l}_{i})=x^{l}_{\text {PU}_{p}}(k_{p})\). Similarly, by setting *N*_{d}=*N*_{p}, *N*_{i}=*N*_{m}, *k*_{d}=*k*_{p}, *k*_{i}=*k*_{m}, *i*_{d}=*i*_{p}, *i*_{i}=*i*_{m}, \(|h^{l}_{\text {PU}_{p}}|\exp \left (j\theta ^{l}_{U_{p}}\right)\), \(\left |h^{l}_{i}\right |=\alpha ^{l}_{M}\left |h^{l}_{\text {MU}_{p}}\right |\), \(\theta ^{l}_{d} = \theta ^{l}_{U_{p}}\), \(z^{l}=z_{p}^{l}\), \(x^{l}_{d}(k^{l}_{d})=x^{l}_{\text {PU}_{p}}(k_{p})\), and \(x^{l}_{i}\left (k^{l}_{i}\right)=x^{l}_{\text {MU}_{m}}(k_{m})\), Eq. (24) becomes Eq. (12).

### 6.2 Throughput without joint ML detection

*k*

_{d}th constellation point is given as follows:

In the same way as in Sec. (5), by appropriate substitutions, Eq. (28) becomes Eqs. (9) and (10).

## Notes

### Acknowledgment and Funding

This work is supported in part by a Grant-in-Aid for Scientific Research (C) under Grant No.16K06366 from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

### Availability of data and materials

The first author have the data and source codes.

### Authors’ contributions

The author contributed to the proposal and evaluation of the written schemes. The author read and approved the final manuscript.

### Competing interests

The author declares that he/she has no competing interests.

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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