## Reduce Complexity in Resource Allocation for Hyper MIMO System with

## Block Diagonalization Precoding Technique

### Maung Sann Maw

### and Iwao SASASE

Dept. of Information and Computer Science, Keio University

3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522 Japan E-mail: sannmaw@sasase.ics.keio.ac.jp, sasase@ics.keio.ac.jp

**Abstract** Hyper Multi-input Multi-output (hyper-MIMO) is considered as a promising technology for the fifth generation (5G) of
wireless communication system. BS is equipped with a large-scale transmit antenna array to serve the multiuser with single-received
antennas for the active users in the system. To improve the system performance, BS must activate some selected users’ receive antennas in
user side for data receiving and make the optimal power distribution. In this paper, we propose a reduced-complexity resource allocation
method for Hyper-MIMO in multiuser system. We consider joint power distribution and user selection based on the signal to interference
plus noise ratio (SINR) conditions of each user in the system. By using block diagonalization precoding technique, SINR status of each user
can be calculated and this value will be applied in the user selection process and resource allocation for the selected users in the system to
increase the total sum-rate of multiuser hyper-MIMO system. We show that the proposed scheme offers enormous reduction in complexity
while ensuring the acceptable performance when compared with optimal resource allocation scheme in the system.

**Keywords** *Hyper MIMO, Complexity, Resource Allocation*

**1.** **Introduction **

The 5th generation (5G) broadband wireless access network, which targets data rate over 10Gbps, is expected to be ready for launch by 2020 [1]. Therefore, it is necessary to find the most promising technology to fulfill the requirements of 5G data rate in near future. On the other hand, hyper-MIMO systems have a great potential to improve the capacity without increasing system bandwidth or transmission power for the wireless communications [2].

A hyper-MIMO refers to a system where base station is equipped with a large number of antennas (e.g. tens or hundreds) communicates with several single-antenna users in the same time-frequency domain [3]. The capacity can be improved and increased by using aggressive spatial multiplexing techniques in hyper MIMO. The basic premise behind hyper-MIMO is to reap all the benefits of conventional MIMO, but on much greater scale. [4]. It was shown that the large antenna array at the BS can provide high degrees of freedom and thus increase the system capacity, link reliability, and radiated-energy efficiency.

Moreover, hyper MIMO can simultaneously serve multiple user equipements (UEs) within a cell using the same time-frequency domain and thus, the spectral efficiency is dramatically improved. However, user selection is also critical important factor for optimizing the overall performance of hyper-MIMO systems. Recently, many selection schemes have been proposed for hyper-MIMO systems in [5-7]. By exploiting the instantaneous CSI

of candidate UEs, Lee and Sung proposed the semi orthogonal user selection method in [6], and Xu et al. developed a greedy user selection scheme in [7] to be applied in FDD-based hyper-MIMO downlink scenarios. By contrast, Liu et al. considered a pair of low-complexity user selection methods for TDD-based hyper MIMO downlink scenarios [5]. The two most well-known user scheduling methods are; round-robin scheduling [8] and random user selection (RUS).

In MIMO, precoding is important in order to avoide the co-channel interference across parallel channels at same time-frequency domain. One of the most promising precoding techniques is block diagonalization (BD), which supports multiple stream transmissions. BD is known as one of the practical precoding techniques that can successfully eliminates co-channel interference in downlink MU hyper-MIMO) system. Moreover, the capacity of hyper-MIMO can still be improved by using optimal transmit power distribution in different users.

Therefore, the optimal method based on the exhaustive brute force search (BFS) finds the best user set over all possible combination of UE’s antenna in the user side. And this method will use the optimal power allocation to each user based on their channel condition and SINR inforation. But, this BFS solution cannot be implemented in practice even for small size systems because of its very high computational complexity.

Therefore, we do the research work to find the suboptimal scheme for user selection in MU hyper-MIMO system to reduce the complexity as well as to improve the sum-rate in this system. And the

### ― 1 ―

This article is a technical report without peer review, and its polished and/or extended version may be published elsewhere.

Copyright ©2017 by IEICE 一般社団法人 電子情報通信学会 信学技報

THE I NSTI TUTE OF ELECTRONI CS, I EI CE Tec hni c al Repor t

I NFORMATI ON AND COMMUNI CATI ON ENGI NEERS CS2017- 54 ( 2017- 11)

proposed user selection scheme is done based on the SINR information with singular value decomposition (SVD) for the BD precoding techniques and user grouping to select the best user user set in the system. The simulation results show that proposed scheme can give the acceptable capacity with less complexity in calculation when compared with conventional optimal scheme and random selection scheme.

**2. System Model**

We consider a single cell MU hyper-MIMO
downlink channel in TDD system consisting of BS,
which has antennas set N and user set K with single
receive antenna for each user in the network as
illustrated in Fig. 1. Moreover, BS can know the
perfect channel state information (CSI) because of
channel reciprocity in TDD system. The main
channel between all of the transmitting antennas and
receiving users can be represented by a channel
matrix HHN,K = [*hi j*]*i*∈N* _{, j}*∈K

*,*where

_{}

_{}

_{represents a channel coefficient between a user }

*i* and transmit antenna *j* and it is assumed to be a
quasi-static to block fading as well as independent
and identically distributed (i.i.d) with zero mean
circularly symmetric Gaussian (ZMCSG) Rayleigh
fading channel.

It is well known that the optimal strategy for
achieving the sum capacity in a MIMO broadcast
channels is full combination search in user set.
However, its implementation is impractical because
of high complexity when number of users is
increased in hyper-MIMO system. Therefore, we
assume the hyper-MIMO system with *S *(_{}_{}_{}_{ RF }

chains in BS to use for data transmission to the
selected users in the network. BS performs the user
scheduling U ( U*=S*) users among the K users
within the cell to be served simultaneously. To
maximize the sum-rate in data transmission, BS
creates one user set U, to be scheduled in the system.

For the given U, the channel between the
transmit antennas (*j*) and selected schedule users (*i*)
can be represented by a channel matrix HUN = [*hi j*].

For user selection in our system, we try to improve not only for reduction of the complexity but also for

increasing of capacity throughput (sum-rate) with
lower user interferences in the system. To achieve
the higher capacity throughput with good SINR value,
we consider using block diagonalization (BD)
precoding technique. In this case, the transmitted
signal vector _{U} _{ for }_{i}t h_{ user in set }U_{ is formed by }

the product of desired scalar signal U

and the
associated precoding vector _{U} _{ for user }_{i }_{in the }

set U and can be expressed as follows:

_{U} _{}_{}_{U} _{U} (1)
where, _{U} _{}_{}_{}_{}

is the precoding vector for *it h* user

in set U and it satisfies _{U} _{}_{}_{. Moreover, }_{}_{U}

must be satisfied U U and _{}UU .. U

and *P* represent the transmit power assigned to *it h*

user in set U and total transmit power for set U, respectively.

By using BD precoding vector _{U}_{, }_{i}t h_{ user in set }

U can avoid the interference from other users at set U in the same frequency and time domain as shown below:

U

_{U}= 0 for all *i* ≠ *k* and _{}U , _{}_{}U_{ (2) }

where, U denote the *it h* row of HU,N. Therefore,

the received signal U* *at the *it h* user in set U can be

written as:

U UUUU _{}U_{}UU (3)

*ni* is the additive white Gaussian (AWGN) noise
with zero mean and variance *N0* at receiver of *it h* user

in set U.

The signal to interference plus noise ratio (U

) at

*it h* user in set U can be described as:

U

_{U} U_{U}

_{U}

U_{U}

_{}U

(4)

U

U
_{U}

_{} _{}_{}_{U}

U_{} U

_{U}

where, U defined by
_{U}

denotes the SNR for *it h*

user in set U. Finally, the broadcasting sum-rate for

the given set N and U can be calculated as:

_{} UN _{}U_{} U

(5)

**3.** **Problem Formulation **

Antenna selection can be formulated as an optimization problem and can be expressed as follows:

_{U,N}_{}UN

UN

_{}

_{}U U (6)

subject to

U_{}_{} (7)

U

_{}U (8)

**Fig 1 Propos ed MU hype r-MIMO Syst em Model**

In the proposed method, BD precoding technique
will be used and it requires for calculating the
beamforming vector of a user *i, * _{, BS first }

calculates the null space of the remaining (*K*−1)
users, except user *i*. The null space of a matrix can be
obtained by using singular value decomposition
(SVD) method [9].

Constraint in (7) ensures that the number of
selected users U does note exceed the number of
available RF chains *S* in BS as being restricted by (7).
Constraint (8) ensures that the summation of transmit
power of all users’ data signal must be within the
allowed total transmit power *P* in BS. And optimal
water filling power distribution will be applied in
selected user set in the system.

The formulated problem is a combinatorial problem, which involves finding the optimal sets of users represented by binary integer variables. The only known technique that can find the optimal solutions to this problem is the exhaustive search [10] and corresponding computation complexity grows exponentially as K increases. Therefore, suboptimal scheme is presented in next section.3 to be used in real implementation for joint antenna and user selection for MU hyper-MIMO system.

**4.** **Proposed Resource Allocatoin Scheme **

In this section, we explain about a reduced complexity user-scheduling scheme that can be implemented in practical MU hyper-MIMO downlink systems. The proposed scheme aims to approach the maximum achievable sum-rate by exploiting both multiuser diversity gain and the spatial selectivity gain offered by the user scheduling.

The proposed scheme will use SINR information from BD precoding techniques to select the best suitable users in the selection and the complexity of selection will be limited by eliminating the lower SINR users in the selection of users. After that we get the final set of user in the system for optimal transmit power distribution among users in the

system. At last, optimal water-filling power distribution technique will be applied on the final selected user set to achieve higher capacity throughput in the system.

The proposed selection algorithm is described in Algorithm 1.

**5.** **Simulation Results **

The simulation parameters are shown in Table.1. We compare the performances of scheme in terms of the CPU usage time and the sum-rate for the hyper-MIMO system. To show the various scenarios for the MU hyper-MIMO system, we consider the cases with different user numbers in the given system. CPU usage time for the calculation complexity results are normalized by using the smallest value in each complexity performance figures to clarify the ratio of complexity for each scheme.

As shown in Fig. 2, sum-rate performance of the proposed scheme is higher than the random selection method. When total number of users is not much greater than number of antennas in the system, the proposed scheme and random selection scheme have not many options to choose the good user set to avoid the user correlation in the system. Therefore the performances of the optimal scheme is better at the lower number of user region in the simulation. Any way, the proposed scheme can give better capacity result compared with the random selection scheme as shown in Fig. 2.

Fig.3 shows the complexity performance in real CPU usage time in the MATLAB simulation platform for the proposed scheme and other two conventional schemes. In this case, the fixed antenna number N=10 and RF chains S=10 are using with the increasing user numbers from 10 to 50As shown in this figure, the CPU usage of the proposed scheme is

** **

1 "!) ! " !

("

2 !'!) ! " ! " , "

U Ui n i t

4/1(+(_{0( }

3 "! ! -

. " & " !" *

4 ! ! !UUs o r t_{ $! ! ! }

! _{U}

(≤≤ U _{) } *

5 ! ! " ! ! ! ! ! "

! $ " ! ! " #

! & !*

6 ,$ ! $!, ! ! $

!"! !" $ !

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A

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**T able. 1** Simulation Par ame te rs

Channe l Rayl ei gh F adi ng

S NR 5dB C el l S ingl e N umber of pa cke ts in

s im ula ti on

15000

F rame s /P ac ket 5
N umber of us er i n s yst em *Var i es (10 to 50) *

N umber of R F c hai ns i n B S *10 *
N umber of ant en na in B S *10 *

**Fig.2 C ompariso n o f sum- rat e f or large r number of**
**var ious ****K **_{w it h }**S =1 0 a n d N= 1 0**

much lower than that of the optimal brute force search. On the other hand, the proposed scheme’s CPU usage time is nearly same as that of the random selection scheme. This is because the proposed scheme is eliminating the lower SINR users from the selection process.

Fig.4 and 5 also show the performances of proposed scheme with smaller number of users, which are increasing, from 15 users to 35 users in the system. We achieve the similar results as larger number of vairous users case in Fig.4 and 5. In these results we can see that the total sum-rate of proposed method is higher than that of random selection method. As stated in Fig.5, the CPU usage time of the proposed method is much lower than the optimal selection method and nearly equal to the conventional random selection method. Therefore, it can be concluded that the proposed method can give reduced complexity in calculation time for the selection process while maintaing the acceptable total sum-rate for MU hyper-MIMO system.

**6.** **Conclusion **

We have presented the low complexity antenna selection scheme for downlink MU hyper-MIMO TDD system. To achieve the reduce complexity in antenna selection while maintaining acceptable capacity in the system, the proposed scheme relied on SINR calculation based on BD precoding techniques and SVD method. The optimal water-filling transmit power distribution for each user is applied in the selected user list to improve the data sum-rate in the proposed system. The proposed scheme can perform successfully to increase the capacity with lower

complexity for various numbers of users in the system. It has been shown using simulations that the proposed scheme outperforms the conventional optimal scheme and random selection scheme in CPU usage time while maintaining the acceptable capacity in MU hyper-MIMO communication.

**Acknowledgements **

This work is partly supported by the Grant in Aid for Scientific Research (No.17K06440) from Japan Society for Promotion of Science (JSPS).

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**Fig.4 C ompariso n o f sum- rat e f or sm alle r number of**
**var ious ****K **_{w it h }**S =1 0 a n d N= 1 0**

**Fig.5 C ompariso n of calculat ion com ple xit y f or**
**sm alle r number of var ious ****K**_{ w it h }**S =1 0 a n d N= 1 0**

**Fig.3 C ompariso n of calculat ion c omplexity f or**
**large r number of var ious ****K **_{w it h }**S =1 0 a n d N =1 0 .**