First IEEE International Conference on Communications in China: Signal Processing for Communications (SPC)
Interference Alignment through Antenna Switching to Improve Quality of Service in Wireless Networks †
Nan Zhao† , Hongxi Yin† , F. Richard Yu‡ , and Hongjian Sun§ Lab of Optical Communications and Photonic Technology, School of Information and Communication Engineering, Dalian University of Technology, Dalian, China ‡ Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, K1S 5B6, Canada § Department of Electronic Engineering, King’s College London, London, WC2R 2LS, UK Email: {zhaonan, hxyin}@dlut.edu.cn; richard
[email protected];
[email protected]
Abstract—Interference alignment (IA) is a promising technique that can effectively eliminate the interference in multiuser wireless communication networks. However, in traditional IA schemes, the signal to interference plus noise ratio (SINR) may decrease greatly when the desired signal and the interference are aligned in the similar directions by IA. Consequently, the bit error rate (BER) will be large, and the quality of service (QoS) can become unacceptable. In this paper, a novel IA scheme based on antenna switching at the receivers is proposed to improve the SINR of the received signal, and guarantee the QoS in IA wireless networks. In the proposed scheme, one reconfigurable antenna is equipped at each receiver to switch between two modes, and the best channel coefficients are selected to maximize the minimal SINR of the desired signal of all the receivers. Simulation results are presented to show that the proposed IA scheme can significantly improve the QoS of IA wireless networks.
I. I NTRODUCTION Interference alignment (IA) is an emerging technology in controlling the interference contamination in a way such that all the interference seen by a receiver falls into one signal subspace and leaves the remaining subspace interference-free [1], [2]. In IA schemes, precoding matrix should be suitably selected to constrain all the interference into one half of the signal space at each receiver and leave the other half with no interference for the desired signal. Then the expected signal can be obtained by using suitably selected interference suppression matrix [3]. Degrees of freedom (DoFs) and capacity of K-user interference networks through IA are studied in [1], and iteration algorithms to obtain the solution of IA based on the reciprocity of wireless networks are proposed in [4]. To mitigate the influence of the delayed channel state information (CSI), an IA scheme based on channel prediction is proposed using linear predictors [5]. Due to the excellent performance This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 61071123, the Fundamental Research Funds for the Central Universities, China Postdoctoral Science Foundation under 2012M510806, and Open Fund of State Key Laboratory of Advanced Optical Communication Systems and Networks (Peking University), P. R. China.
978-1-4673-2815-9/12/$31.00 ©2012 IEEE
of IA, it has been successfully applied to cognitive radio and femtocell wireless networks [6]–[9]. Although IA schemes can eliminate interference in wireless networks, the signal to interference plus noise ratio (SINR) may decrease greatly when the desired signal and the interference are aligned in the similar directions by IA. Consequently, the bit error rate (BER) will be large under these channel coefficients, and the quality of service (QoS) can become unacceptable [3]. Thus, this problem should be solved effectively to make IA suitable for practical networks. Unfortunately, only a few research works have focused on improvement of QoS in IA wireless networks [4], [10]. In addition, traditional IA schemes usually seek perfect interference alignment to eliminate the interference completely, however, when the interference is completely eliminated, the SINR of the desired signal may not be maximal. In [4], a max-SINR IA algorithm is proposed to obtain the maximal SINR of the desired signal, and thus can optimize the QoS of the communication network. However, the improvement of QoS in [4] is not significant, and it is still difficult to apply the scheme to practical systems. An improved blind interference alignment is proposed in [10], and it can increase the SINR of the desired signal by changing power allocation in transmitted streams. However, this scheme may only be used for blind IA scenarios [11]. In this paper, we propose a novel interference alignment scheme based on antenna switching [12], [13] to improve the QoS of IA wireless networks. The motivations are as follows. Antenna switching is usually done in a selfish manner, in which each receiver chooses the mode that enables the greatest signal strength for itself [14]. On the other hand, IA usually operates in an un-selfish manner, in which all the users seek the best precoding and interference suppression matrices to achieve the optimal capacity or QoS of the whole system. If we combine antenna switching and IA, better performance can be achieved. Specifically, we use a reconfigurable antenna that is equipped at each receiver to switch between these two modes. Best channel coefficients are selected to maximize the minimal SINR of the desired signals, and thus the QoS of the
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user, respectively. x[k] (n) is the transmitted signal vector of d[k] DoFs at the kth transmitter. N[k] (n) is a d[k] × 1 AWGN vector corresponding to each DoF at the kth receiver, with zero mean and each element’s variance equal to σ 2 . The interference in the interference alignment network can be efficiently eliminated only when the following conditions are satisfied U[k] (n)H H[kj] (n)V[j] (n) = 0, ∀j = k, rank U[k] (n)H H[kk] (n)V[k] (n) = d[k] . Fig. 1.
II. S YSTEM D ESCRIPTION Consider a K-user multiple-input multiple-output (MIMO) interference channel as shown in Fig. 1, and the kth transmitter and receiver are equipped with M [k] and N [k] antennas, respectively. The received signal at the kth receiver can be represented as K
H[kl](n)X[l](n)+Z[k](n), ∀k ∈ {1, 2, ..., K},
l=1
(1) where, at the discrete-time instant n, Y[k] (n) and Z[k] (n) are the N [k] ×1 received signal vector and additive white Gaussian noise (AWGN) vector at the kth receiver, respectively. X[l] (n) is the M [k] ×1 signal vector transmitted by the lth transmitter, and H[kl] (n) is the N [k] × M [k] matrix of channel coefficients between the lth transmitter and the kth receiver. When IA is performed through using matrices V[k] (n) and [k] U (n) at the time instant n, k ∈ {1, 2, ..., K}, and the DoFs achieved by the kth user is d[k] . The received signal at the kth receiver can be denoted as y[k] (n) = U[k] (n)H H[kk] (n)V[k] (n)x[k] (n) K + U[k] (n)H H[kl] (n)V[l] (n)x[l] (n) + N[k] (n),(2) l=1,l=k [k]
(4)
With each transmitting and receiving node having M antennas, the capacity of the whole MIMO interference network can be denoted as [4]
Interference alignment system model.
network can be improved effectively. Simulation results are presented to show the effectiveness of the proposed scheme. The rest of the paper is organized as follows. In Section II, we present the system model. The decrease of the SINR and QoS in IA networks is analyzed in Section III. In Section IV, the proposed IA scheme based on antenna switching is presented. In Section V, simulation results are given and discussed. Finally, conclusions and future work are presented in Section VI. Notition: Id represents the d × d identity matrix. AT and H A are the transpose and conjugate transpose of matrix A, respectively. |a| is the absolute value of a.
Y[k](n) =
(3)
where V (n) and U[k] (n) are M [k] × d[k] precoding matrix and N [k] × d[k] interference suppression matrix of the kth
C (SNR) =
KM log(SNR) + o(SNR), 2
(5)
so that the capacity per user is M 2 log(SNR) + o(log(SNR)). Here signal-to-noise ratio (SNR) is defined as the total transmit power of all the transmitters in the network when the local noise power at each receiver is normalized to unity. The o(log(SNR)) term can be negligible compared with log(SNR) when SNR is high. III. A NALYSIS OF SINR D ECREASE IN IA W IRELESS N ETWORKS Although IA schemes can eliminate the interference in wireless networks completely through the precoding matrix V and interference suppression matrix U constrained by (3) and (4), the SINR may decrease greatly when the desired signal and the interference are aligned in the similar directions by IA. For example, in the simple IA model [1] shown in Fig. 2, there are K=3 users, and M=N=2 antennas are equipped at each transmitter and receiver. At receiver 1, the interferences are H[12] v[2] x2 and H[13] v[3] x3 , which should be different from the direction of the desired signal H[11] v[1] x1 , and they should be aligned at the same direction. Thus we can assume that H[12] v[2] = [a2 b2 ]T , H and
[13] [3]
v
T
= [a3 b3 ] ,
a3 a a2 = = . b2 b3 b
(6) (7) (8)
The desired signal at receiver 1 is H[11] v[1] x1 , and we define that H[11] v[1] = [c d]T . (9) Assume the angle between the direction of the desired signal [a b]T and the direction of interferences [c d]T is θ, and it can be calculated as ac + bd √ . (10) θ = arccos √ a2 + b2 · c2 + d2
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Fig. 3.
Fig. 2. Interference alignment system on the 3-user MIMO interference channel with 2 antennas at each transmitter and receiver.
Then, the acute angle δ between two directions can be expressed as θ, 0 ≤ θ ≤ π/2 δ= (11) π − θ, π/2 < θ ≤ π. Theorem 1: When δ becomes larger, the received power of the desired signal becomes larger, and the higher QoS can be achieved. Proof: Set | arccos(θ)|=f , 0 ≤ f ≤ 1. f becomes smaller when δ is larger, and f can be calculated as f=√
a2
|ac + bd| √ . + b2 · c2 + d2
From (12), we can obtain
2 (ad − cb) = 1 − f 2 a2 + b2 c2 + d2 .
(12)
Especially, when δ=π/2 and f = 0, the received power of the desired signal is maximal, and the QoS is relatively high; when δ=0 and f = 1, the received power of the desired signal is almost zero, and the QoS of the communication system cannot be guaranteed. From the analysis above, it can be shown that the SINR of the received signal in IA schemes is sometimes extremely low, and the QoS is poor. Hence, we should improve the SINR of the IA scheme when it is applied to practical wireless systems. IV. IA S CHEME BASED ON A NTENNA S WITCHING From the analysis in section III, we can see that the SINR of the received signal will decrease greatly when the directions of desired signal and interferences are similar. Consequently, the QoS of the IA network cannot be guaranteed when it is used in practical wireless systems. In this section, we propose a novel IA scheme based on antenna switching. In our scheme, one of the antennas at each receiver is replaced by a reconfigurable antenna [12], [13] as shown in Fig. 3. A. Reconfigurable Antenna and Objective Function
(13)
To eliminate the interference at receiver 1, the interference suppression vector u[1] should be T a −b √ . (14) u[1] = √ a2 + b2 a2 + b2 Therefore, the desired signal at receiver 1 can be calculated through u[1] as −b a x1 , y1 = c √ + d√ (15) a2 + b2 a2 + b2 and its power can be calculated as 2 −b a P1 = c√ + d√ a2 + b2 a2 + b2 2 (ad − cb) = 2 2
a + 2b 2 c + d2 . = 1−f
Conceptual depiction of reconfigurable antenna in our scheme.
The reconfigurable antenna can switch among 2 preset modes, and the channel coefficients between all the antennas at the transmitters and this reconfigurable antenna change values in the two modes. In Section III, the QoS of the IA scheme is analyzed by the angle between the direction of the desired signal and the direction of the interferences. This method is lucid but inaccurate. In this section, the SINR of the desired signal is utilized to measure the QoS of the IA scheme. The SINR of the desired signal in IA scheme is defined and can be referred to [4]. Suppose there are K receivers in the IA scheme, and thus there are 2K available solutions because each reconfigurable antenna has two preset modes. We propose the objective function of the IA scheme based on SINR for the optimal solution as
popt−SINR = arg max min{SINRk , k=1, ..., K}, p=1, ..., 2K , p
(16)
Therefore, from (16) we can conclude that when δ becomes larger, f becomes smaller, the received power of the desired signal becomes larger, and thus the higher QoS can be achieved. I
k
(17) where SINRk is the SINR of the desired signal of the kth receiver. The problem described in (17) is a max-min problem, and its computational complexity is 2K . When K is relatively small, brute-force search can be utilized to enumerate all possible candidates for the solution. When K becomes larger, it is an NP-hard problem, and the metaheuristic algorithms,
309
Fig. 4. The illustration of the timing structure of one frame in the proposed IA scheme.
e.x., ant colony optimization (ACO) and genetic algorithm, can be applied to obtain the optimal solution with lower computational complexity [15]–[17]. Another method to obtain the optimal solution is measured by the maximal total capacity of the network, and the objective function of the IA scheme based on maximal capacity can be described as K K popt−Capacity = arg max , (18) Ck , p = 1, ..., 2 p
Fig. 5. Interference alignment system on a 3-user MIMO interference channel based on antenna switching through reconfigurable antenna.
60
k=1
Conventional IA scheme Maximal−capacity antenna switching IA Maximal−SINR antenna switching IA
55
where Ck is the capacity of the kth user, which can be defined as P [k] [kk] [kk]H [k] R = log Id[k] + [k] H H (19) . d
50 45 40 bit/s/Hz
The performance of these two methods will be compared in Section V. B. Proposed IA Scheme Based on Antenna Switching The timing of a frame in the proposed IA scheme is illustrated in Fig. 4, and the proposed scheme in the transmission of one frame can be represented by the following steps: 1) All the reconfigurable antennas are switched to Mode 1 in duration τ1 in Fig. 3. The channel coefficients corresponding to the Mode 1 of the reconfigurable antennas are estimated and available for IA. 2) All the reconfigurable antennas are switched to Mode 2 in duration τ2 in Fig. 3. The channel coefficients corresponding to the Mode 2 of the reconfigurable antennas are estimated and available for IA. 3) The objective function defined in (17) or (18) is calculated in duration τ3 , and the solution with the maximal value is set as the optimal channel coefficients and applied to IA. 4) The frame of information is transmitted in duration τ4 using IA scheme with the optimal channel coefficients obtained in Step 3. 5) The transmission of one frame is finished, and another frame will be started. Assume that the duration of one frame is T, and it can be denoted as T = τ1 + τ2 + τ3 + τ4 , (20) where τ1 , τ2 and τ3 τ4 . Thus τ1 , τ2 and τ3 can be ignored. The length of τ4 is dependent on the level of the channel fading.
35 30 25 20 15 10 5 0
0
5
10
15
20 25 30 SNR (dB)
35
40
45
50
Fig. 6. Capacity comparison of the IA scheme, maximal-capacity antenna switching IA scheme, and maximal-SINR antenna switching IA scheme.
V. S IMULATION R ESULTS AND D ISCUSSIONS In our simulations, we consider a MIMO interference network consisting of K=3 users in Fig. 5. M =2 antennas are equipped at each transmitter, and one ordinary antenna and one reconfigurable antenna are equipped at each receiver based on antenna switching manner. All the channels are under Rayleigh fading. First, the capacity of the whole IA network is analyzed. The average capacity of the IA network based on antenna switching with maximal-SINR solution defined in Equ. (17), and that of the IA network based on antenna switching with maximal-capacity solution defined in Equ. (18) are compared in Fig. 6.
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A novel interference alignment scheme based on antenna switching through reconfigurable antenna has been proposed to improve the QoS of IA wireless networks, and two objective functions for antenna switching are presented. Using computer simulations, we have demonstrated that the proposed antenna switching IA scheme aiming at maximizing the SINR of the desired signal can improve the QoS in IA wireless networks significantly. When the number of users in the system becomes large, the computational complexity increases exponentially. Thus in our future work, we will do further research on the antenna switching based IA scheme to balance between the QoS and computational complexity.
−1
10
−2
BER
10
−3
10
R EFERENCES
−4
10
Conventional IA scheme Maximal−capacity antenna switching IA Maximal−SINR antenna switching IA 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Eb/N0 (dB)
Fig. 7. BER comparison of the IA scheme, maximal-capacity antenna switching IA scheme, maximal-SINR antenna switching IA scheme, and SISO scheme.
From the simulation results in Fig. 6, we can see that the capacity of the IA network is increased through antenna switching, and the capacity of the maximal-capacity antenna switching IA scheme is a little larger than that of the maximalSINR scheme. However, capacity is not the most important thing we should consider, and QoS is more important in some practical networks. In wireless communication networks, QoS is usually measured by BER of the users. Thus, the BER achieved by these schemes is compared in Fig. 7. For all the users, phase shift keying (PSK) is applied, and coherent detection is performed at the receivers. The basedband symbol rate is 2Mbps. From the simulation results in Fig. 7, we can see that the BER performance of the two proposed antenna switching IA schemes is much better than the conventional IA scheme. Although the capacity of the network is the largest when maximal-capacity solution of antenna switching IA scheme is applied, its BER is still relatively high. The BER of the maximal-SINR solution of antenna switching IA scheme is much lower than that in the other two schemes when maximalcapacity solution is applied. Thus, we can conclude that the QoS of the IA system can be improved significantly with the proposed maximal-SINR antenna switching IA scheme, and it is more suitable for practical utilization than the conventional IA scheme and the maximal-capacity antenna switching IA scheme. VI. C ONCLUSIONS AND F UTURE W ORK In this paper, we have analyzed the problem of the SINR and QoS degradation in conventional IA schemes, which makes them difficult to utilize in practical wireless networks.
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