2014 Sixth International Conference on Wireless Communications and Signal Processing (WCSP)
Opportunistic Interference Alignment Networks for Simultaneous Wireless Information and Power Transfer through User Selection ‡
Nan Zhao‡ , F. Richard Yu† , and Victor C.M. Leung§
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 Electrical and Computer Engineering, the University of British Columbia, Vancouver, BC V6T 1Z4 Canada Email:
[email protected];
[email protected];
[email protected] †
Abstract—Interference alignment (IA) is an emerging technology for interference management. However, the received signal-to-interference-plus-noise ratio (SINR) may decrease in IA. Opportunistic IA (OIA) schemes can provide more opportunities for the users to access the network and improve the performance; nevertheless, the unselected users remain idle, which is a waste of resource. Thus in this paper, simultaneous wireless information and power transfer (SWIPT) in OIA networks is studied. As the unselected users in OIA networks can be treated as energy harvesting (EH) terminals, an OIA user selection (OIAUS) algorithm is proposed to optimize the SWIPT performance through user selection, according to the information-transmission (IT) and EH performance as well as the requirements of users. To further reduce the complexity, a random complexity-reduced OIAUS algorithm is designed to make a tradeoff between performance and complexity. Simulation results are presented to show the effectiveness of the proposed algorithms. Index Terms—Interference alignment, simultaneous wireless information and power transfer, opportunistic communications, user selection.
I. I NTRODUCTION Interference management is becoming one of the key issues in wireless networks, and interference alignment (IA) is a promising solution that emerges recently [1]. In IA networks, the transmitted signals of all the users are cooperatively precoded so that the interferences at the unintended receivers can be aligned into certain subspaces, and the remaining interference-free subspaces can be harnessed to obtain the desired signal at the receivers. Although the performance of IA in solving the interference problem in multiuser wireless networks is remarkable, there are still some challenges when it is utilized in practical systems. One of the key issues is the signal-to-interference-plus-noise ratio (SINR) decrease [2], [3]. A Max-SINR algorithm was proposed for IA in [2] to maximize the SINR of the received signal, instead of perfect alignment of the interferences. Zhao et al. [3] analyzed the SINR decrease of IA in detail, and This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 61201224, China Postdoctoral Science Foundation Special Funded Project under 2013T60282, and the Fundamental Research Funds for the Central Universities under DUT14QY44.
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proposed an antenna-switching IA scheme to improve the throughput through using reconfigurable antennas. On the other hand, when there are much more users than an IA network can support wish to access the spectrum, the idea of opportunistic communications can be adopted. In the existing opportunistic IA (OIA) schemes [4]–[6], multiuser diversity was exploited by selecting some of the users to form the instantaneous IA network opportunistically according to the status of the channels, and the throughput or SINR performance of the network can also be improved significantly. However, the unselected users is inactive at the time slot, and thus it is a waste of resources in the network. Recently, green communications have attracted a lot of interests [7], [8], and energy harvesting (EH) is an effective method to make communications greener [9]. Radio-frequency (RF) signals can transmit information and carry energy simultaneously, and thus simultaneous wireless information and power transfer (SWIPT) is becoming a vigorous aspect of EH [10], [11], in which RF signals are used as a vehicle for the transferring of both the information and power. In IA wireless networks, the interferences are eliminated instead of reutilization, which is a waste of energy, and some initial work on SWIPT in IA networks was conducted in [12]. In this paper, we study SWIPT in OIA networks, and an OIA User Selection (OIAUS) algorithm is proposed. In the OIAUS algorithm, some of the users are optimally selected as IA users to transmit information, while the remaining users are dedicated to EH. The complexity of the OIAUS algorithm is analyzed, and a Random Complexity-Reduced OIAUS (RCROIAUS) algorithm is designed to reduce the complexity of the OIAUS algorithm. Notation: Id represents the d × d identity matrix. A† and |A| are the Hermitian transpose and determinant of matrix A, respectively. ∥a∥2 and ∥A∥2 are the ℓ2 -norm of vector a and matrix A, respectively. λmax (A) means the maximal eigenvalue of the matrix A. |a| is the absolute value of complex number a. CM ×N is the space of complex M × N matrices. CN (a, A) is the complex Gaussian distribution with mean a and covariance matrix A.
Thus the desired signal of user s can be assumed to be [ss] received through a d[s] × d[s] effective channel matrix H , [s]† [ss] [s] U H V , and (1) can be simplified as [ss] [s]
y[s] = H
x
+ z[s] ,
(4)
where z[s] = U[s]† z[s] , following CN (0, Id[s] ). Based on the analysis above, the transmission rate of user s in the OIA network can be expressed as Pt [ss] [ss]† R[s] = log2 Id[s] + [s] H H (5) . d
Fig. 1.
Demonstration of an OIA network for SWIPT.
II. S YSTEM D ESCRIPTION A. OIA Networks with Multiuser Diversity Consider a K-user interference channel with M [k] and N [k] antennas equipped at the kth transmitter and receiver, respectively, and only S users are selected to form an instantaneous IA network at each time slot as in Fig. 1, where S < K, and S can be determined by the feasible conditions of linear IA [13]. Perfect channel state information (CSI) of the network is assumed to be available at all the transceivers. If linear IA is adopted to avoid interferences among users, the received signal with d[s] data streams at the selected receiver s ∈ S can be represented as ∑ y[s] (n)= U[s]†(n)H[sj](n)V[j](n)x[j](n)+U[s]†(n)z[s](n),(1) j∈S
where S is the set containing the selected S users to form [s] [j] the IA network at the nth time slot. H[sj] (n) ∈ CN ×M denotes the channel gain matrix from transmitter j to receiver s at the nth time slot. For a symmetric network, each entity of H[sj] (n) can be assumed to be independent and identically distributed (i.i.d.) CN (0, ap ), where 0 < ap ≤ 1, which can be determined according to the signal attenuation due to path loss. Block fading channel is adopted in this paper, and for clarity, the time slot number n is henceforth suppressed unless [s] [s] [s] [s] stated otherwise. V[s] ∈ CM ×d and U[s] ∈ CN ×d are the unitary precoding and decoding matrices of user s, respectively. x[s] is composed of d[s] data streams of user s [s] with power constraint Pt = Pt for the symmetric network. [s] z[s] ∈ CN ×1 represents received noise vector with distribution CN (0, IN [s] ) at receiver s. When the OIA is feasible, the interferences at each receiver can be assumed to be completely eliminated when [2] U[s]† H[sj] V[j] = 0, ∀j ̸= s, j, s ∈ S, ) ( rank U[s]† H[ss] V[s] = d[s] , ∀s ∈ S.
(2) (3)
Since this paper mainly concentrates on the information and power transfer in the OIA networks instead of degrees of freedom (DoFs), it is assumed that there is only one data stream for each user in the rest of this paper. The conclusion for the situation with more streams can be easily extended. Besides, symmetric networks are considered, and thus all the users have the same parameters, i.e., M [k] = M, N [k] = N, d[k] = 1, ∀k = 1, 2, . . . , K. The instantaneous IA at each time slot is feasible, i.e., condition (2) is met, only when (6) is satisfied [13]. M + N ≥ S + 1. (6) The performance of information transmission (IT) of the OIA network is analyzed as in Theorem 1. Theorem 1: In the conventional OIA network, the upper bound of the instantaneous rate of user s at a certain time slot can be expressed as ( ( )) [s] Rup = log2 1 + Pt λmax H[ss]† H[ss] . Proof: See Appendix A. In the conventional OIA network [6], S users are selected to optimize the throughput of the network at each time slot. From Theorem 1, we can know that the instantaneous rate of a certain selected user s in the OIA network will approach the [s] upper bound Rup as the number of available users K becomes larger due to the multiuser diversity. B. Wireless Power Transfer in the OIA Networks The selected users in the conventional OIA network are scheduled to transmit information through forming an instantaneous IA network, while the other unselected users are remaining idle, which is a waste of the wireless resources. It is natural that the unselected users can harvest power from the selected transmitters, and recharge their batteries. Thus in the proposed OIA network for SWIPT as in Fig. 1, the selected IA users are transmitting information at the time slot, while the other unselected users are dedicated to EH. Each transmitter of the OIA wireless network is assumed to have a constant power source, while all the receivers need to replenish energy through WPT to support the information decoding (ID) and recharge the batteries. The received signal of unselected user u in the OIA network at a certain time slot can be expressed as ∑ [uj] [u] b v[j] x[j] + z[u] , u ∈ b y = H / S. (7) j∈S
Assume that the harvested energy due to the background noise is negligible and can be ignored. Thus its harvested power can be expressed as
∑
b [uj] [j] [j] 2 b [u] = ζ Q
H v x 2
j∈S
∑
b [uj] [j] 2 = ζPt / S,
H v , u ∈ j∈S
2
NETWORK FOR
2
j∈St
(8)
where S is the set containing the selected S users at the time b [uj] denotes the channel gain from the selected user slot, and H j to the unselected user u. ζ ∈ (0, 1) is a constant representing the loss in the energy transducer for converting the harvested energy to electrical energy to be stored [10]. ζ is assumed to be 0.2 throughout this paper for the convenience of analysis. III. U SER S ELECTION IN THE OIA
¯ kk , u[k]† H[kk] v[k] . Q b [u] is the harvested power of the where h unselected user u. When the solution Ct of user selection is b [u] can be expressed applied in which user u is not selected, Q as
∑
b [uj] [j] 2 b [u] = ζPt Q / St , (12)
H v , u ∈
SWIPT
A. User Selection From the above analysis in Section II, we can know that the performance of IT and EH in the OIA network is quite different for each user, i.e., the transmission rate of a certain user may be quite high while its harvested power may be extremely low according to the instantaneous channel status of the network, vice versa. Besides, the requirements of IT and EH of the users in the network may be different according to the kinds of service and status of batteries. Thus the S users should be selected opportunistically to form an IA network at each time slot as in Fig. 1. The selected IA users can transmit information at the time slot, and the remaining users can harvest power at the receivers with their transmitters sleeping. Due to the selection of S IA users out of all the K candidates at each time slot, the number of combinations of the selected users for the problem can be calculated as ( ) K T = . (9) S Define C = {C1 , C2 , ..., CT } is the set that consists of all the available solutions of user selection to the problem. We should choose the S users according to the optimal solution Copt , through which the best performance can be achieved. In the OIA scheme, different objective functions can be defined, according to which, the optimal solution can be calculated. In this section, the user selection should be performed according to the instantaneous IT and EH performance, and the specific requirements of each user. Thus we propose an OIAUS algorithm for SWIPT based on the following optimization problem of (10) (on the next page). In (10), ε[k] = 1 and ε[k] = 0 means the kth user in the network ∑ is selected or is not selected as an IA user, K respectively. k=1 ε[k] = S guarantees that only S users are selected to form IA at each time slot. R[k] is the transmission rate of user k when it is selected in the OIA network, and it can be expressed as ( 2 ) hkk , (11) R[k] = log2 1 + Pt ¯
where St is the set containing the selected S users when b [uj] denotes the channel gain solution Ct is adopted, and H from the selected user j to the unselected user u. Remark 1: For a certain user k in the OIA network, its transmission rate R[k] when selected and its harvested power b [k] when not selected, are quite different when the adopted Q solution Ct is changed. For a given user k, we assume that it is selected when either Ct1 or Ct2 are performed. The vectors u[k] and v[k] are quite different for user k with Ct1 and Ct2 , because all the selected users should cooperate to form the IA, and different combination of selected users will result in different IA model. Thus R[k] will surely change with different combinations of b [k] . selected users. This is also true for Q [k] 0 ≤ α ≤ 1 in (10) represents the weight given to the requirement of transmission rate user k, and 1 − α[k] is the corresponding weight to its harvested power. For a certain user in the network, its value of α means the relationship between the requirements of IT and EH. β is a constant to balance the rate and power with unit bit/s/Hz/W. When α becomes larger, it represents that the battery power of this receiver is sufficient and the required rate of this user is high; when α becomes smaller, it means low-power status of the battery of the receiver, and the rate of this user is not so high. Especially, α[k] can be defined as [k]
Rtar
α[k] =
[k]
[k]
,
(13)
Rtar + βQtar [k]
[k]
where Rtar is the target transmission rate of user k, and Qtar is the target harvested power of the kth user. Thus 1 − α[k] can be expressed as [k]
1 − α[k] =
βQtar [k]
[k]
.
(14)
Rtar + βQtar
The optimal solution of user selection Copt can be achieved when the optimization problem in (10) is solved, and it is a combinatorial optimization. Through the OIAUS algorithm, both of the IT and EH performance of the network can be optimized according to the specific requirements of the users. B. Computational Complexity of the OIAUS Algorithm and Random Complexity-Reduced OIAUS Algorithm The OIAUS algorithm defined as in (10) is a combinatorial optimization problem, the number of available combinations of the selected users in the OIAUS algorithm is listed in Table I according to (9). From the results, it is shown that the computational complexity of the OIAUS algorithm increases dramatically with larger K and smaller value of |S/K − 0.5|, when brute-force search is adopted to enumerate
{ max ε[1] ,ε[2] ,...,ε[K]
s.t.
K ∑
[k]
[k] [k]
α R ε
+
K ( ∑
1−α
[u]
)
b [u]
(
βQ
1−ε
[u]
)
} (10)
u=1
k=1 [k]
ε ∈ {0, 1}, K ∑ ε[k] = S.
k = 1, 2, . . . , K,
k=1
21
TABLE I T HE N UMBER OF AVAILABLE C OMBINATIONS OF THE S ELECTED U SERS IN THE OIAUS A LGORITHM K=4
K=5
K=6
K=7
K=8
K=9
K=10
S=3
4
10
20
35
56
84
120
S=4
1
5
15
35
70
126
210
S=5
1
S=6 S=7 S=8 S=9
6
21
56
126
252
1
7
28
84
210
1
8
36
120
1
9
45
1
10
Average Sum Rate (bits/s/Hz)
T
20
19
OIAUS, a=1 OIAUS, a=0.5
18
OIAUS, a=0 IA, Random User Selection
17
16
15
14
3
4
5
6
7
8
9
10
K
In the proposed RCR-OIAUS algorithm, only a portion of the available solutions in the set C is randomly chosen to be searched. Define Tr is a positive integer that is smaller than T , and Tr solutions are randomly selected in C to form the reduced set Cr to be used in the RCR-OIAUS algorithm. The procedure of the RCR-OIAUS algorithm can be described in Algorithm 1. Algorithm 1 - RCR-OIAUS
1: 2: 3: 4: 5: 6:
A time slot starts. Randomly choose Tr possible solutions in C, and form the reduced set of Cr . Calculate the IA solutions of each combinations in Cr . Replace the set C with Cr in (10), and obtain the optimal solution of user selection Copt−r according to (10). Perform SWIPT in the network in the remaining time of the slot. The time slot ends. Back to Step 1.
The computational complexity of the RCR-OIAUS algorithm is only TTr of that in the OIAUS algorithm, and its IT and EH performance is close to that of the OIAUS algorithm when Tr is large enough. Thus Tr should be set with a tradeoff between the computational complexity and performance.
0.7 OIAUS, a=0 OIAUS, a=0.5 OIAUS, a=1 IA, Random User Selection
0.6 Average Harvested Power (Pt )
all the possible combinations of the selected users to obtain the optimal solution. The computational complexity of the OIAUS algorithm should be reduced when it is applied to the practical systems. Besides, as the number of available solutions becomes larger, the performance improvement of the OIAUS algorithm gets more and more trivial. Therefore we propose an RCR-OIAUS algorithm for SWIPT in IA networks to reduce the computational complexity of the OIAUS algorithm.
Fig. 2. Comparison of the average sum rate of the OIA network with different number of K and different values of α using OIAUS algorithm.
0.5
0.4
0.3
0.2
0.1
0
3
4
5
6
7
8
9
10
K
Fig. 3. Comparison of the average harvested power of the OIA network with different number of K and different values of α using OIAUS algorithm.
IV. S IMULATION R ESULTS AND D ISCUSSIONS In the simulation, S = 3, and 2 antennas are equipped at each transceiver. Rayleigh block fading is adopted, and perfect CSI is assumed to be available at each node. ap = 0.05, ζ = 0.2, β = 100, and the transmit SNR is set to 30dB, which is the ratio between transmit power and the background noise. The average sum rate and harvested power with different number of K and different values of α using OIAUS algorithm are compared in Fig. 2 and Fig. 3, respectively. From the results in Fig. 2 and Fig. 3, we can know that both of the average sum rate and harvested power will increase with
17.2
0.6
17
16.6
0.55
16.4 16.2 16
0.5
15.8 15.6
Sum Rate in RCR−OIAUS
15.4
Sum Rate in OIAUS (Tr=120)
15.2
Sum Power in RCR−OIAUS Sum Power in OIAUS (Tr=120)
15 14.8
0.45
Average Harvested Power (Pt )
Average Sum Rate (bits/s/Hz)
16.8
0
20
40
60 Tr
80
100
0.4 120
Fig. 4. Comparison of the average sum rate and harvested power performance in the RCR-OIAUS algorithm with different values of Tr .
where the effective channel can be expressed by the complex inner product of the two vectors. Based on Cauchy-Schwarz inequality, we can get that
¯ hss ≤ u[s] H[ss] v[s] = H[ss] v[s] , (16) 2 2 2
because u[s] 2 = v[s] 2 = 1. According to the definition of the operator norm, we can obtain that
[ss] [s]
v
H
[ss] [ss] [s]
2 = max v
H = max
H
. (17)
v[s] 2 2 v[s] ̸=0 ∥v[s] ∥2 =1 2 Due to the definition of spectral norm, we can also obtain √
) (
[ss] (18)
H = λmax H[ss]† H[ss] . 2
larger K when the OIAUS algorithm is performed, and the performance of the OIAUS algorithm is much better than that when the users are randomly selected in the OIA network. When α = 1, the throughput of the OIA network is optimized; when α = 0, the harvested power is optimized; when α = 0.5, the throughput and power are jointly optimized, and a tradeoff can be made between rate and power with different values of α. When α = 0.5 and K is larger than 6, the throughput performance of the OIAUS algorithm is almost unchanged with different K, this is because optimizing power is becoming more important when K is large in this situation, and increasing K will not achieve better rate performance. The average sum rate and harvested power performance of the RCR-OIAUS algorithm when K = 10 and S = 3 are also compared in Fig. 4 with different values of Tr . From the results, it is shown that the performance of RCROIAUS algorithm is becoming better with larger Tr , and the performance enhancement is becoming slower with larger K. When Tr gets close to T in the OIAUS algorithm, the performance of the RCR-OIAUS algorithm is getting to that of the OIAUS algorithm. V. C ONCLUSIONS In this paper, we have presented an OIA scheme for SWIPT, in which only a portion of the users are selected as IA users and the other receivers are dedicated to EH. We proposed an OIAUS algorithm for SWIPT in OIA networks. In the proposed algorithm, the IA users are selected to optimize the SWIPT performance according to the requirements of the users. To reduce the complexity, we proposed an RCR-OIAUS algorithm, in which the searching set of the available solutions is randomly reduced. Simulation results were presented to show the effectiveness of the proposed algorithms. A PPENDIX A P ROOF OF T HEOREM 1 Proof: The effective channel of user k when only 1 stream is transmitted can be denoted as ⟩ ⟨ ¯ ss , u[s]† H[ss] v[s] = u[s] , H[ss] v[s] , (15) h
Thus we can conclude that ( 2 ) R[s] = log2 1 + Pt ¯ hss ( ( )) [s] ≤ log2 1 + Pt σ 2 λmax H[ss]† H[ss] = Rup , (19) [s]
where Rup is the upper bound of the instantaneous transmission rate of user s at a certain time slot. R EFERENCES [1] V. R. Cadambe and S. A. Jafar, “Interference alignment and degrees of freedom of the K-user interference channel,” IEEE Trans. Inf. Theory, vol. 54, no. 8, pp. 3425–3441, Aug. 2008. [2] K. Gomadam, V. R. Cadambe, and S. A. Jafar, “A distributed numerical approach to interference alignment and applications to wireless interference networks,” IEEE Trans. Inf. Theory, vol. 57, no. 6, pp. 3309–3322, Jun. 2011. [3] N. Zhao, F. R. Yu, H. Sun, A. Nallanathan, and H. Yin, “A novel interference alignment scheme based on sequential antenna switching in wireless networks,” IEEE Trans. Wireless Commun., vol. 12, no. 10, pp. 5008–5021, Oct. 2013. [4] J. H. Lee and W. Choi, “Opportunistic interference aligned user selection in multiuser MIMO interference channels,” in Proc. IEEE Globecom’10, pp. 1–5, Miami, FL, Dec. 2010. [5] B. C. Jung and W. Y. Shin, “Opportunistic interference alignment for interference-limited cellular TDD uplink,” IEEE Commun. Lett., vol. 15, no. 2, pp. 148–150, Feb. 2011. [6] Y. He, H. Yin, F. R. Yu, and N. Zhao, “Performance improvements of interference alignment with multiuser diversity in cognitive radio networks,” in Proc. WCSP’13, pp. 1–5, Hangzhou, China, Oct. 2013. [7] F. R. Yu, X. Zhang, and V. C. M. Leung, Green Communications and Networking. CRC Press, 2012. [8] N. Zhao, F. R. Yu, and H. Sun, “Adaptive energy-efficient power allocation in green interference alignment wireless networks,” IEEE Trans. Veh. Technol., to be published. [9] D. Gunduz, K. Stamatiou, N. Michelusi, and M. Zorzi, “Designing intelligent energy harvesting communication systems,” IEEE Comm. Mag., vol. 52, no. 1, pp. 210–216, Jan. 2014. [10] R. Zhang and C. K. Ho, “MIMO broadcasting for simulatneous wireless information and power transfer,” IEEE Trans. Wireless Commun., vol. 12, no. 5, pp. 1989–2001, May 2013. [11] K. Huang and E. Larsson, “Simultaneous information and power transfer for broadband wireless systems,” IEEE Trans. Signal Proc., vol. 61, no. 23, pp. 5972–5986, Dec. 2013. [12] N. Zhao, F. R. Yu, and Victor. C.M. Leung, “Simultaneous wireless information and power transfer in interference alignment networks,” in Proc. IWCMC’14, pp. 1–5, Nicosia, Cyprus, Aug. 2014. [13] C. Yetis, T. Gou, S. A. Jafar, and A. Kayran, “On feasibility of interference alignment in MIMO interference networks,” IEEE Trans. Signal Proc., vol. 58, no. 9, pp. 4771–4782, Sep. 2010.
