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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 1, NO. 5, OCTOBER 2012
Energy-Efficient Cooperative Relaying in Heterogeneous Radio Access Networks Gubong Lim, Student Member, IEEE, and Leonard J. Cimini, Jr., Fellow, IEEE
Abstract—Recently, much attention has been given to heterogeneous networks where a mobile device is capable of accessing multiple random access networks (RANs), where each RAN operates on a different carrier frequency with a different transmission bandwidth, using multi-radio platforms embedded in the device. In this letter, we investigate the efficient use of multiple radio access technologies (RATs) to improve the energy efficiency in cooperative networks. Considering the circuit power consumption of each RAT, we study energy-efficient bestselect relaying and show that the proposed scheme significantly outperforms traditional best-select relaying as well as direct communications. Index Terms—Energy efficiency, heterogeneous, multi-radio, cooperative communications.
I. I NTRODUCTION
I
N present-day systems, different radio access technologies (RATs) often coexist in a network, and advanced mobile devices are able to communicate through any of these RATs (e.g. WLAN, WCDMA, and LTE in a smartphone), in what is called a multi-radio access (MRA) system [1]-[2]. Recently, resource allocation in a MRA system has been investigated using multiple RATs simultaneously to optimize the spectral efficiency [3]-[4]. Instead of simultaneous utilization of multiRATs, in [5], the RAT is chosen to maximize the network capacity subject to QoS constraints. Previous works in this area, however, have not considered the effect of circuit power consumption in the analysis. The energy consumption issue in wireless communication is an extremely important one. Thus, there has been growing research interest on the energyefficient design of wireless communication systems, including consideration of the system-wide energy consumption [6]. In [7], an energy-efficient, best-select, cooperative relaying scheme is studied and the optimal mode switching technique is proposed using a single RAT. In [8], using a realistic battery model, energy-efficient relay selection and power allocation strategies are studied. In this letter, we study energyefficient, best-select, relaying in a heterogeneous cooperative radio access network where each relay node is capable of utilizing multiple RATs. We consider the optimal relay and RAT selection problem to maximize the energy efficiency. In addition, optimal and suboptimal adaptive modulation schemes are proposed to further improve the efficiency. Manuscript received May 15, 2012. The associate editor coordinating the review of this letter and approving it for publication was T. Q. S. Quek. The authors are with the Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716 USA (e-mail:
[email protected],
[email protected]). This research has been supported by NSF under Grant No. 1017053. Digital Object Identifier 10.1109/WCL.2012.070312.120366
II. S YSTEM M ODEL In Fig. 1, we illustrate a heterogeneous cooperative radio access network; each source, relay, and destination node is equipped with multiple radio modes (RMs) that use different RATs. We assume that each RM operates on a different carrier frequency and uses a different transmission bandwidth. We consider a best-select relaying scheme, where a single “best” relay, among all the relay nodes, is selected to forward the source message to the destination in a decode-and-forward fashion. The received SNR at relay i using RM j with nominal transmit power Pt is defined as
(i, j) = Pt ˜(i, j)
(1)
where ˜(i, j) = H(i, j)/PN ( j). PN ( j) = N0 B( j) is the noise power in RM j, where N0 is the noise power spectral density and B( j) is the bandwidth of RM j. H(i, j) is the channel power gain from the source to relay i using RM j. We assume that a distance-based path-loss component is included in the channel gain and is given (in dB) as d (2) PL(d) = PLF (d0 ) + 10 log10 d0 where 2 PLF (d0 ) = −10 log10 (3) 4 d0 where d0 is the reference distance, is the path-loss exponent, and is the wavelength ( = c/ f , where c is the speed of light and f is the carrier frequency). Since the carrier frequency is different for different radio modes, we have different values of PLF (d0 ). Then, the decoded set of RM j, D j , is defined as the set of relay nodes that correctly decode the source message in RM j; this set is given as D j = {i|Pmax ˜(i, j) ≥ th (bSR )}
(4)
where Pmax is the maximum transmit power of a relay and th (bSR ) is the required SNR to meet the target bit error probability, pth , with bSR bits/symbol; for M-QAM, this is p 1 bSR th 2 − 1 ln th (bSR ) = − (5) c2 c1 which is obtained by inverting the approximation [9] c2 th pth (b) = c1 exp − b (6) 2 −1 where c1 = 0.2 and c2 = 1.5. After the decoded set is determined, each relay node estimates the channel gain for each RM k in the relay-todestination (RD) link, G(i, k), and the best relay is selected based on an appropriate selection algorithm. The selected relay then forwards the source message to the destination.
c 2012 IEEE 2162-2337/12$31.00
LIM and CIMINI: ENERGY-EFFICIENT COOPERATIVE RELAYING IN HETEROGENEOUS RADIO ACCESS NETWORKS
R
S
Radio mode 1 Radio mode 2 Fig. 1.
477
for the RD link using RM k, respectively. TSR ( j) = b LB( j) and SR TRD (k) = bRDLB(k) are the required transmission times for each link. PC ( j) and PC (k) are the total circuit power consumption for the SR link and the RD link transmissions, respectively. Dividing by TRD (k) and factoring out B(k), we get
D Selected Radio mode
EE(i, j, k) =
No
th (bRD ) G(i,k)
+
bRD th (bSR ) bRD C ( j)bRD + PB( H(i, j) bSR j)bSR
C (k) + PB(k) (10)
Cooperative networks with multi-radio equipped relay nodes.
V. O PTIMAL R ELAY AND R ADIO M ODE S ELECTION
III. C IRCUIT P OWER M ODEL We divide the total power consumption into the power consumed by the transmit power amplifier (PA) and the power consumed by the rest of the circuitry, which we call the “circuit power consumption.” The power consumed in the PA is given as Pt / where is the PA efficiency. In the literature, a constant circuit power consumption has been widely used in the analysis of energy efficiency. Here, we assume that the circuit power consumption consists of two parts: one from the digital circuitry and the other from the RF chain [7] (excluding the PA). We model the digital circuit power consumption as a linear function of the transmission bandwidth; as the bandwidth increases, more computations and baseband processing are required (e.g., increased DSP computation and more frequent memory access). We denote the power consumption from the digital circuitry as PBB, and model it as B re f + (7) PBB = PBB Bre f re f where PBB is the reference digital circuit power consumption, Bre f is a reference bandwidth, and is a proportionality constant (in mW). We also assume that the power consumption for the RF chain, PRF , is a constant. Thus, the total circuit power consumption is given by tx rx tx rx PC = PBB + PBB + PRF + PRF
(8)
The superscripts “tx” and “rx” designate the transmitter and the receiver, respectively. The typical RF chain power contx = P sumption at each end is modeled as PRF DAC + 2Pf il + PLO + rx Pmix and PRF = PADC + 3Pf il + PLO + Pmix + PLNA [7]. PDAC , PADC , Pf il , PLO , Pmix , and PLNA are the power consumption for the D/A and A/D converters, filter, local oscillator, mixer, and low noise amplifier, respectively. IV. E NERGY E FFICIENCY OF B EST-S ELECT R ELAYING In this section, we derive the energy efficiency of bestselect relaying with multi-radio nodes. The energy efficiency (in bits/Joule) using relay i with RM j for the source-to-relay (SR) link and RM k for the RD link for transmitting L bits is EE(i, j, k) = L (PSR (i, j)/ + PC ( j))TSR ( j) + (PRD (i, k)/ + PC (k))TRD (k) (9) (b )P ( j)
(b
)P (k)
N SR N and PRD (i, k) = th RD are where PSR (i, j) = th H(i, j) G(i,k) the required transmit power for the SR link using RM j and
We first consider the case where the constellation sizes used in both links are the same, bSR = bRD = b. Then, the energy efficiency can be simplified to EE(i, j, k) =
b ES (i, j) + ER (i, k)
(11)
(b)No PC ( j) th (b)No PC (k) where ES (i, j) = thH(i, j) + B( j) and ER (i, k) = G(i,k) + B(k) . Here, we note that the first terms in ES (i, j) and ER (i, k) are the required transmission energies and the second terms are the circuit energy consumption. Then, for a fixed constellation size b and a given relay i, maximizing (11) is equivalent to minimizing the total consumption for each link, ES (i, j) and ER (i, k), separately. Then, the optimal RM for the SR link is th (b)No PC ( j) + j∗ = arg min (12) j∈Si H(i, j) B( j)
where Si is the “decoded radio mode set” of relay i, which is the set of radio modes for which relay i correctly decodes the source message; this set is given as Si = { j|Pmax ˜(i, j) ≥ th (b)}
(13)
The RD link optimization problem in the presence of a maximum power constraint is th (b)No PC (k) ∗ + k = arg min (14) k G(i, k) B(k) th (b)PN (k) ≤ Pmax s.t. G(i, k) Then, we find the optimal relay which minimizes the total energy consumption for a given optimal pair of RMs i∗ = arg min (ES (i, j∗ ) + ER (i, k∗ ))
(15)
i
VI. A DAPTIVE M ODULATION WITH O PTIMAL R ELAY AND R ADIO M ODE S ELECTION Adaptive modulation has been shown to be an effective way to improve energy efficiency. Here, we consider the joint optimization of the modulation size with relay and RM selection. We also consider a maximum end-to-end delay constraint, Tmax . Then, the optimization problem becomes max
i, j,k,bSR ,bRD No
th (bRD ) G(i,k)
+
bRD th (bSR ) bRD PC ( j) bRD H(i, j) bSR + B( j) bSR
s.t. TSR (i, j) + TRD (i, k) ≤ Tmax PSR (i, j), PRD (i, k) ≤ Pmax
C (k) + PB(k)
(16)
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IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 1, NO. 5, OCTOBER 2012
TABLE I S YSTEM PARAMETERS
A. Optimal Strategy For fixed RMs j and k of relay i, we obtain the optimal constellation sizes b∗SR and b∗RD by numerical search. In this case, we first fix the bSR and find the corresponding optimal b∗RD . Then, we search all values of bSR which satisfy the constraints to find the optimal constellation size for both links. Thus, (16) is equivalent to max EE(bSR , bRD )
bSR ,bRD
RD bRD min (bSR ) ≤ bRD ≤ bmax RD where bSR max and bmax are the maximum constellation sizes that satisfy the target bit error probability for a given channel gain. L is the minimum constellation bRD min (bSR ) = L Tmax − b B( j) B(k) SR
size for the RD link to meet the delay constraint for a given L bSR . bSR min = max{bmin1 , bmin2 } where bmin1 = Tmax BSR which guarantees that the SR link transmission time is less than Tmax , RD and bmin2 is the minimum bSR such that bRD min (bSR ) < bmax . B. Suboptimal Strategies In this section, we consider three suboptimal strategies. 1) Suboptimal #1: In this scheme, we optimize the constellation size of each link independently. In order to obtain the optimal b∗SR , we first solve the unconstrained optimization; the solution is ˜
(18)
o where K1 = − c NH(i, j) ln(pth /c1 ). Then, the optimal solution 2 with constraints, using (18), is ⎧ outage, for bmax < bmin ⎪ ⎪ ⎪ ⎨b , for bmin ≤ bmax < b˜ max (19) b∗ = ˜ ⎪ b, for bmin ≤ b˜ ≤ bmax ⎪ ⎪ ⎩ bmin , for b˜ ≤ bmin ≤ bmax
˜ ˜ where bmin = bmin1 , bmax = bSR max , and b = bSR . Similarly, we ˜ find bRD which is the solution of the unconstrained optimization problem for a given b∗SR as ˜
K2 (2bRD − 1) + PC(k) b˜ RD = K2 2b˜ RD ln(2)
(20)
o where K2 = − c NG(i,k) ln(pth /c1 ). Then, for a given b∗SR , the 2 optimal solution with constraints has the same form as (19) RD ˜ ˜ with bmin = bRD min , bmax = bmax , and b = bRD . 2) Suboptimal #2: In this case, we restrict the constellation sizes for both links to be equal, i.e., bSR = bRD = b, and find the optimal size. This suboptimal scheme clearly reduces the number of computations compared to suboptimal scheme 1. The optimal constellation size is obtained by using the solution of the unconstrained optimization problem that we solved previously. Then, the optimal solution, b∗ , has a form similar L RD to (19); in this case, bmax = min (bSR max , bmax ) and bmin = BT ¯ max . 1 B¯ = B( j)B(k) = .
B( j)+B(k)
TSR ( j)+TRD (k)
35 % 3.5 20 dBm -174 dBm/Hz 10−4 20 mW 2.0 / 2.4 / 5.0 1.0 / 5.0 / 10.0
(17)
SR s.t. bSR min ≤ bSR ≤ bmax
K1 (2bSR − 1) + PC( j) b˜ SR = K1 2b˜ SR ln(2)
Amplifier efficiency, Path-loss exponent, Maximum power constraint, Pmax Noise power spectral density, N0 Target bit error probability, pth Proportionality constant, Carrier frequency of RM-1/ RM-2/ RM-3, f (GHz) Bandwidth of RM-1/ RM-2/ RM-3, B (MHz)
3) Suboptimal #3: The two suboptimal schemes above require finding the optimal constellation size for each relay i, and the corresponding radio modes, RM j and k, which might require a large number of computations. Thus, we propose another suboptimal scheme where the optimal relay and RMs are first obtained for a fixed modulation size, and the optimal constellation size for each link is found by numerical search. VII. S IMULATION R ESULTS The parameters used in the simulation are given in Table I. We assume that there are M = 5 relay nodes located equidistant from the source and the destination nodes. The proportionality constant, = 20 mW, has been deduced from [10] where the baseband power consumption is projected for current and future wireless communication systems. We assume that tx rx tx rx ≈ PRF = PRF and PBB ≈ PBB = PBB . We can easily extend PRF these results for cases where the power consumptions at the transmitter and the receiver are different. In order to evaluate the energy efficiency, we use the normalized reference power Pre f re f where Pre f = PBB + PRF . Thus, for consumption, = Pmax B → 0, PC ≈ 2 Bre f and for 0, Pc ≈ Pre f . RM 1 is assumed to be the reference system in the simulation. In Fig. 2, we present the energy efficiency (EE) of bestselect (BS) relaying with a fixed 2 bits/symbol for both links. We use a normalized destination distance where the reference distance d0 = 1 meter. We denote BS-O as the optimal BS scheme and BS-C as the conventional BS which ignores the circuit power consumption (PC = 0) and only considers the channel gain and transmission power amplifier. We also plot the EE of direct communications with RM adaptation (DC-O). From the figure, we see that the EE of DC-O is initially higher than for BS, but degrades rapidly with distance due to the lack of diversity gain. Also, we observe that BS-O significantly outperforms BS-C for short distances, and both converge as the distance increases. This is because BS-O chooses the RM and the relay that balance the transmission and circuit power consumption; BS-C, however, only considers the transmission power in RM and relay selection, leading to the performance degradation. For large distances, the EE is mainly affected by the outage performance which makes BS-O select the relay and RMs having the largest channel gains, as for BSC. As increases, the EE of both schemes decreases due to the increased Pre f . Moreover, with a larger Pre f , the power consumption difference between RMs is negligible, which renders BS-O less advantageous compared to BS-C. In Fig. 3, we plot the corresponding probability of the RM that is selected for transmission for BS-O (solid line) and DCO (dashed line). For both, for short distances, even for larger noise power and with path loss, the RM having the higher
LIM and CIMINI: ENERGY-EFFICIENT COOPERATIVE RELAYING IN HETEROGENEOUS RADIO ACCESS NETWORKS
12 10
=0.5 =5.0
0.8
BS−O BS−C DC−O
Prob(RM)
14
1
8 6 4
0.6 RM−1 RM−2 RM−3
0.4
0.2
2 0 100
200 300 400 Normalized Destination Distance
0 100
500
Fig. 2. Energy efficiency of best-select relaying and direct communications in heterogeneous radio access networks for 2 bits/symbol.
bandwidth is selected to reduce the circuit power consumption. However, as the distance increases, the optimal scheme is likely to choose the RM supporting a lower bandwidth, operating on a lower frequency, to meet the target SNR. In Fig. 4, we show the EE of BS and DC with adaptive modulation for = 0.5. The figure shows that adaptive modulation significantly improves the EE compared with a fixed constellation size. Interestingly, we observe that the two suboptimal schemes, BS-Sub1 and BS-Sub2, provide performance close to the optimum. Also, it can be seen that BS-Sub3 with 2 bits/symbol performs worse than that with 4 bits/symbol for short distances. The reason is as follows: For a fixed constellation size, the RM having the largest bandwidth is selected to minimize the circuit power consumption. Thus, with 2 bits/symbol, RM 3, supporting a 10-MHz bandwidth, is likely to be selected for short distances. However, the selected link with the larger bandwidth and path loss leads to a smaller maximum constellation size, which limits the degrees of freedom for adaptive modulation compared to that of the selected link with 4 bits/symbol. For large distances, using a larger constellation size for the selection increases the outage probability, degrading the energy efficiency. In general, BS-O benefits from recognizing the different circuit power consumption characteristics of different radio modes and taking them into account during relay and radio mode selection. Thus, for a fixed circuit power consumption for different radio modes, increasing the number of relay nodes or the maximum power constraint improves the energy efficiency of both schemes, typically for large distances. However, it does not change the relative performance between them. The performance of BS-O only converges to that of BSC when Pre f BBre f or ≈ 0, for which the circuit power consumption difference between RMs is negligible. VIII. C ONCLUSION We considered optimal relay and radio mode selection in heterogeneous cooperative radio access networks, and demonstrated that it is critical to take the circuit power consumption into account in the selection algorithm design to improve the energy efficiency. We also showed that the energy efficiency can be further improved by employing adaptive modulation.
200 300 400 Normalized Destination Distance
500
Fig. 3. Probability of the selected radio modes of the optimal best-select relaying (solid) and direct communications (dashed) for 2 bits/symbol.
30 Energy Efficiency (Mbits/Joule)
Energy Efficiency (MBits/Joule)
16
479
25 20 15
BS−O BS−Sub1 BS−Sub2 BS−Sub3−2bit BS−Sub3−4bit BS−C DC−O
10 5 0 100
200 300 400 Normalized Destination Distance
500
Fig. 4. Energy efficiency of best-select relaying using various adaptive modulation schemes in a heterogeneous radio access network. ( = 0.5).
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