Proportional fairness analysis of massive MIMO Two-tier multiuser downlink with subchannel pairing

doi:10.1016/j.phycom.2017.05.001

Physical Communication

Volume 24, September 2017, Pages 9-18

https://doi.org/10.1016/j.phycom.2017.05.001 Get rights and content

Abstract

This paper presents a proportional fairness throughput analysis of a millimeter wave massive multiple-input multiple output (MIMO) small base station (SBS)-assisted downlink with subchannel (SC) pairing. We derive an analytical expression for evaluating the average logarithmic throughput with SC-pairing and proportional fairness in two-tier network with amplify-and-forward (AF) and decode-and-forward (DF) SBSs. Analytical expressions are derived for the probability density function (PDF) of logarithmic throughput, and the average logarithmic throughput with statistical channel state information (CSI) based gain at AF SBS. It has been shown that the percentage error between simulation and analytical results decreases with increase in number of SC $N$ and number of antennas, and is upper bounded by 0.28% and 0.79% when $N \geq 16$ for AF and DF SBSs, respectively.

Introduction

The continuously increasing data traffic from smart phones, tablets, and other mobile devices, would soon overload the existing cellular infrastructure. It has been forecasted that the next-generation wireless networks will have to support 1000 times more capacity as compared to the today’s capacity [1]. In fifth generation (5G) wireless communication systems, the unused or lightly used millimeter wave along with the massive multiple-input-multiple-output (MIMO) communications enable the additional access to the 30–300 GHz bands [2]. These higher frequencies increase the system capacity but on the other side it suffers from the higher path losses [2]. The use of the multi-tier system can alleviate the path losses problem by providing possible line of sight or fewer multi-paths to the destination [3].

Recently, the need for high data rates has evoked the need of massive multiple-input multiple-output (MIMO) antenna systems [4], [5], [6]. It is expected that Long Term Evolution-Advanced (LTE-A) will remain as the baseline technology for wide area broadband coverage also in the 5G era. Work on further functions for critical communications will continue in Release 13 and beyond, for example, in the area of enabling relays (relaying between in-coverage and out-of-coverage devices) and push-to-talk type functionality [7].

New mobile applications that mandate data rates in the range of several Gigabits per second (Gbps) cannot be handled with current technology. To handle such large data volumes, higher frequency bands spans from 6 to 95 GHz must be employed [8], [9]. 5G wireless technology will start using these frequency bands that promising technology will emerge in 2020 [10]. Moreover, 5G technology shall comply with their predecessor mobile technologies. The compatibility condition was also placed on LTE-A technology which has to cope with previous mobile generations [11].

It is expected that 5G will support more than 10 Gbps at the beginning stage. This rate will continue increasing to hit Ultra data rates, e.g., 50 Gbps. Intensive research and work have been conducted to figure out the amount of data rates that 5G frequency bands can provide to user equipment (UE). For example, in [12], a data rate of 1 Gbps can be reached at the UE in outdoor line-of-sight (LOS) channel located around at 1 km distance and around 200 m in the outdoor non-LOS (NLOS) channel. Huang et al. reported that a data rate of up to 115 Gbps can be realized in a point-to-point transmission [13]. In [14] the authors perform a simulation on system comprises simply two stream MIMO employing 64-QAM at 72 GHz to reveal a very promising results including peak rates in excess of 15 Gbps. This humongous data rates as was previously mentioned can be achieved using higher frequency bands or millimeter waves (mmWave) frequencies. Cellular networks that utilizes mmWaves can support more users compared to Long Term Evolution-Advanced (LTE-A) technology. However, network nodes tuned at mmWaves experience small coverage area problem as well as outdoor penetration difficulty.

5G technology will deploy several innovative approaches to overcome the higher frequency bands limitations and thus data rates challenges [15]. The main challenges in mmWave cellular networks found in link margin operation. This margin can be achieved by enabling beamforming approach in high directional antenna arrays installed at 5G macro base station, a technology knows as massive MIMO [16], [6], [17]. The beamforming will minimize the interference between users using the same bandwidth in the same cell [18].

Massive MIMO have many folds of which are enhancement of networks throughput, improvement of radiated energy efficiency, significant reduction in latency, low hardware cost, etc. In spite of achieving these folds, massive MIMO still faces many challenges and problems such as distribution processing algorithms, antennas synchronization and computational complexity [4], [19]. A further study on the impact of modulation schemes along with the coordination interference for massive MIMO systems in 5G technology will draw researchers attentions. Base station (BS) densification is an effective methodology to meet the requirements of 5G wireless networks resulting in two-tier or multi-tier communications [20]. It is evident that in 5G networks, there will be deployments of a large number of low power BS, relays, and machine-to-machine (M2M) communication links. The espousal of multiple tiers in the cellular network architecture will result in better performance in terms of throughput, coverage, and energy efficiency, provided that the inter-cell and intra-cell interferences are well managed in time and frequency domains. In addition to interference management, subchannel mapping between two hops further enhances the performance in terms of throughput and coverage area.

This paper is organized as follows: Section 2 summarizes the related work. Section 3 presents the system model. Section 4 is about the problem formulation for the paired-SC proportional-fair throughput. Performance analysis of the paired-SC proportional-fair throughput in a two tier mmWave massive MIMO downlink with AF SBS and DF SBS is given in Section 5 and Section 6, respectively. Comparisons of the analytical and simulation results are provided in Section 7, followed by the conclusions in Section 8.

Section snippets

Related work

The key issue in a two-tier wireless heterogeneous systems is the way in which the two channels are selected. Ordered SC-pairing has been proven as an optimal solution for SC pairing problem. There are several works which provide exact or approximate closed form analytical expressions for end-to-end signal-to-noise-ratio (SNR), bit error rate (BER), symbol error rate (SER), outage probability, outage capacity, and ergodic capacity with ordered SC-pairing. But there is no such work that deals

System model

Consider a system model in which the main base station (MBS) with $N_{m}$ -antenna transmits to $K$ single antenna users with the help of $N_{s}$ -antenna SBS as shown in Fig. 1. SBS receives data in one time slot and transmits in other time slot and the transmission completes in two time slots. The CSI of all wireless links in a cell is assumed to be perfectly known to the MBS and SBS [36], [37], [38], [39]. The CSI of the $N$ SCs for the backhaul and access channels are given by $Backhaul Channel : H = [h_{1}, h_{2}, \dots, h$

Evaluation of paired-SC proportional-fair throughput

In this section, we present the order statistics based proposed exact evaluation of the multiusers’ PF throughput in SBS-assisted two-tier downlink.

E2E PDF and CDF for AF SBS

For notational simplicity, we drop the subscripts of $α_{n}$ and $β_{k, n}$ here and re-write the Eq. (13) as $Γ = \frac{N_{m} N_{s} α}{1 + Q / β}$ where $Q = N_{m} {\bar{γ}}_{m}$ . Let $q = 1 + Q / β$ , where $q > 1$ because $Q > 0$ and $β > 0$ . Using order statistics and function of random variables method we get the density function of $q$ [30], $f_{q} (q) = \frac{Q}{{(q - 1)}^{2}} \sum_{i = 0}^{n - 1} \frac{a_{i}}{{\bar{γ}}_{s}} e^{- \frac{Q b_{i}}{(q - 1) {\bar{γ}}_{s}}}, for q > 1$ where $a_{i} = N (\binom{N - 1}{n - 1}) (\binom{n - 1}{i}) {(- 1)}^{i}$ and $b_{i} = (i + N - n + 1)$ . Similarly, the density function of $α$ is given by $f_{α} (α) = \frac{1}{N_{m} N_{s}} \sum_{j = 0}^{n - 1} \frac{a_{j}}{{\bar{γ}}_{m}} e^{- \frac{b_{j}}{N_{m} N_{s} {\bar{γ}}_{m}} α} .$ The CDF of end-to-end ordered SNR in (19) of the

E2E PDF and CDF for paired-SC PF throughput in massive MIMO DF SBS

In case of DF SBS, the end-to-end SNR is at user $k$ in n-MSP is given as $Γ_{k, n}^{D F} = min (N_{m} N_{s} α_{n}, N_{s} β_{k, n}) .$ The CDF of end-to-end SNR can be expressed as $F_{Γ_{k, n}}^{D F} (Γ) = F_{α} (Γ) + F_{β} (Γ) - F_{α} (Γ) F_{β} (Γ) = \sum_{j = 0}^{n - 1} \frac{a_{j}}{b_{j}} (1 - e^{- \frac{b_{j}}{N_{m} N_{s} {\bar{γ}}_{m}} Γ}) + \sum_{j = 0}^{n - 1} \frac{a_{j}}{b_{j}} (1 - e^{- \frac{b_{j}}{N_{s} {\bar{γ}}_{s}} Γ}) - \sum_{j = 0}^{n - 1} \sum_{i = 0}^{n - 1} \frac{a_{i} a_{j}}{b_{i} b_{j}} (1 - e^{- \frac{b_{i}}{N_{m} N_{s} {\bar{γ}}_{m}} Γ}) (1 - e^{- \frac{b_{j}}{N_{s} {\bar{γ}}_{s}} Γ})$ and the corresponding PDF is given by $f_{Γ_{k, n}}^{D F} (Γ) = \frac{1}{N_{m} N_{s} {\bar{γ}}_{m}} \sum_{j = 0}^{n - 1} a_{j} e^{- \frac{b_{j}}{N_{m} N_{s} {\bar{γ}}_{m}} Γ} + \frac{1}{N_{s} {\bar{γ}}_{s}} \sum_{j = 0}^{n - 1} a_{j} e^{- \frac{b_{j}}{N_{s} {\bar{γ}}_{s}} Γ} - \frac{1}{N_{s} {\bar{γ}}_{s}} \sum_{j = 0}^{n - 1} \sum_{i = 0}^{n - 1} \frac{a_{j} a_{i}}{b_{j}} (1 - e^{- \frac{b_{j}}{N_{m} N_{s} {\bar{γ}}_{m}} Γ}) e^{- \frac{b_{i}}{N_{s} {\bar{γ}}_{s}} Γ} - \frac{1}{N_{m} N_{s} {\bar{γ}}_{m}} \sum_{i = 0}^{n - 1} \sum_{j = 0}^{n - 1} \frac{a_{i} a_{j}}{b_{i}} (1 - e^{- \frac{b_{j}}{N_{s} {\bar{γ}}_{s}} Γ}) e^{- \frac{b_{j}}{N_{m} N_{s} {\bar{γ}}_{m}} Γ} .$

Numerical results and comparisons

In this section we present analytical and simulation results obtained for the PF throughput in a two-tier mmWave massive MIMO system. These results are calculated using the end-to-end PDF derived in (35), (37) with AF and SF SBS, respectively. The analytical and simulation results assume perfect time and frequency synchronization of MBS, SBS and users terminals. In the simulation setup, we take $K = 10$ , $N_{m} = N_{s} = 64$ , ${\bar{γ}}_{m} = {\bar{γ}}_{m} = 10 dB$ , $N = 16$ otherwise stated. We generate 10 000 independent exponential

Conclusions

In this paper, we present analytical results for the end-to-end proportional fair throughput for massive MIMO multiuser AF and DF SBS-assisted downlink transmission with ordered SC-pairing. We derive the maximum logarithmic throughput density function and the average proportional fair sum throughput. The derived expression of sum of PF throughput can be helpful in getting insight for end-to-end throughput dependence on various parameters like per hop SNR, MBS or SBS transmit powers, MBS and SBS

Irfan Ahmed (M’10, SM’16) received the B.E. Electrical Engineering degree and the M.S. Computer Engineering degree from University of Engineering and Technology, Taxila, Pakistan, in 1999 and 2003, respectively, and the Ph.D. degree in Telecommunication Engineering from the Beijing University of Posts and Telecommunications, Beijing, China, in 2008.

Currently, he is working as associate professor in Taif University, KSA. He was post-doctoral fellow with Qatar University from April 2010 to March

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Moreover, the demand for wireless traffic is expected to increase thousand fold by 2020 due to the requirement of high speed data services, lower latency, high spectral efficiency, massive connectivity and green communications [1,2]. Millimeter (mm) wave [3] and massive multiple input multiple-output (MIMO) [4] are some of the key techniques proposed in recent times to meet the preceding requirements. In particular, massive MIMO system, where each base station (BS) contains an array spanning hundreds of antennas serving tens of users concurrently emerge as a key concept for the next generation wireless systems.
In this paper, we present a robust beamforming design to examine the weighted sum-rate maximization (WSRM) problem in a multicell massive MIMO downlink system for 5G communications. This work assume imperfect channel state information (CSI) by adding uncertainties to channel matrices with worst-case models i.e. singular value uncertainty model (SVUM) and ellipsoidal uncertainty model (EUM). In SVUM, WSRM problem is formulated subject to the transmit power constraints. While, the problem is devised in EUM by alternatively considering its dual power minimization problem subject to the worst-case signal-to-interference-plus-noise ratio (SINR) constraints for all mobile stations. The designed problem for both SVUM and EUM are known as non-deterministic polynomial (NP) problem which is difficult to solve. We propose an iterative algorithm established on majorization minimization (MM) technique that solves and achieves convergence to stationary point of these two problems. In EUM, the convergence point is obtained after converting the infinite number of SINR constraints into linear matrix inequalities (LMI) by employing S-Procedure. Extensive numerical results are provided to show that the proposed iterative algorithm significantly increases performance in terms of sum-rate and also attains faster convergence as compared with the conventional polynomial time algorithm.
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Currently, he is working as associate professor in Taif University, KSA. He was post-doctoral fellow with Qatar University from April 2010 to March 2011, where he worked on two research projects, wireless mesh networks with Purdue University, USA, and radio resource allocation for LTE with Qtel. He has also been involved in National ICT Pakistan funded research project “Design and development of MIMO and Cooperative MIMO test-bed” at Iqra University, Islamabad, Pakistan, during 2008 to 2010. His research interests include wireless LAN (WLAN) medium access control (MAC) protocol design and analysis, cooperative communications, MIMO communications, performance analysis of wireless channels, energy constrained wireless networks, cognitive radio networks, and radio resource allocation. He is an author of more than 25 International publications.

Dr. Irfan served as session chair of the IEEE Wireless Communications, Networking and Mobile Computing conference held in Shanghai, China, in September 2007, IEEE ICC 2016. He is an active reviewer of IEEE, Springer, and Elsevier journals, and conferences. He is an associate editor of IEEE Access journal.

^☆: This paper was presented in part at the IEEE International Conference on Communications, Kuala lumpur, Malaysia, May 2016.

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Full length articleProportional fairness analysis of massive MIMO Two-tier multiuser downlink with subchannel pairing☆

Abstract

Introduction

Section snippets

Related work

System model

Evaluation of paired-SC proportional-fair throughput

E2E PDF and CDF for AF SBS

E2E PDF and CDF for paired-SC PF throughput in massive MIMO DF SBS

Numerical results and comparisons

Conclusions

Millimeter-wave gigabit broadband evolution toward 5G: Fixed access and backhaul

IEEE Commun. Mag.

An overview of signal processing techniques for millimeter wave MIMO systems

IEEE J. Sel. Top. Signal Process.

On the performance of relay aided millimeter wave networks

IEEE J. Sel. Top. Signal Process.

Massive MIMO for next generation wireless systems

IEEE Commun. Mag.

An overview of massive MIMO: Benefits and challenges

IEEE J. Sel. Top. Signal Process.

Scaling up MIMO: Opportunities and challenges with very large arrays

IEEE Signal Process. Mag.

3gpp system standards heading into the 5g era

Eurescom Message Mag.

Spectrum occupation and perspectives millimeter band utilization for 5G networks

Millimeter-wave beamforming as an enabling technology for 5G cellular communications: Theoretical feasibility and prototype results

IEEE Commun. Mag.

Millimeter-wave massive MIMO: the next wireless revolution?

IEEE Commun. Mag.

Massive MIMO in the UL/DL of cellular networks: How many antennas do we need?

IEEE J. Sel. Areas Commun.

Modulation formats and waveforms for 5G networks: Who will be the heir of OFDM?

IEEE Commun. Mag.

Millimeter-wave cellular wireless networks: Potentials and challenges

Proc. IEEE

Evolution toward 5G multi-tier cellular wireless networks: An interference management perspective

IEEE Wirel. Commun.

Performance analysis of dual-hop OFDM relay system with subcarrier mapping in nakagami- m fading

IEICE Tans. Commun.

Performance analysis of spectrally efficient amplify-and-forward opportunistic relaying scheme for adaptive cooperative wireless systems

Wirel. Commun. Mobile Comput.

Performance evaluation of OFDM amplify-and-forward relay system with subcarrier permutation

IEICE Trans. Commun.

Outage probability of opportunistic amplify-and-forward relaying in nakagami-m fading channels

Proc. ETRI J.

On the SEP of cooperative diversity with opportunistic relaying

IEEE Commun. Lett.

Full length article
Proportional fairness analysis of massive MIMO Two-tier multiuser downlink with subchannel pairing☆