Device-to-Device (D2D) Communication in Cellular Network - Performance Analysis of Optimum and Practical Communication Mode Selection
Device-to-Device (D2D) Communication in Cellular Network - Performance Analysis of Optimum and Practical Communication Mode Selection
Device-to-Device (D2D) Communication in Cellular Network - Performance Analysis of Optimum and Practical Communication Mode Selection
Abstract—In a cellular network system one way to increase interference levels in the system lead to higher system capacity
its capacity is to allow direct communication between closely and spectrum efficiency.
located user devices when they are communicating with each On the other hand, there are lots of possible practical
other instead of conveying data from one device to the other
via the radio and core network. The problem is then when limitations for D2D such as: 1) probability of local com-
the network shall assign direct communication mode and when munication might be low, 2) propagation channel between
not. In previous works the decision has been done individually devices is ”worse” than propagation channel between a BS
per communicating device pair not taking into account other and devices (mainly due to difference in antenna heights
devices and the current state of the network. We derive means for and antenna gains) and 3) interference to and from in-band
getting optimal communication mode for all devices in the system
in terms of system equations. The system equations capture cellular mode users. Probability of local communication of all
information of the network such as link gains, noise levels, signal- communication in the system should be relatively high to have
to-interference-and-noise-ratios, etc., as well as communication a real reason for direct communication. Thus services and use
mode selection for the devices. Using the derived equations cases that would provide possibility for D2D communication
performance bounds for the cellular system where D2D com- have high importance. Finally, in a system where there are both
munication is an additional communication mode are illustrated
via simulations. Further, practical communication mode selection cellular communication mode and D2D mode users accessing
algorithms are used to evaluate their system performance against the same spectrum, the interference situations are different
the achievable bounds. Analysis show the usability of the system compared to a conventional cellular system.
equations and the potential of having D2D operation integrated Hsieh et al. show that using the peer-to-peer network model
into a cellular system when there is enough local communication in cellular wireless data networks is a promising approach
occurring.
when the network model is complemented with appropriate
mechanisms [4]. They propose a hybrid network model in
I. I NTRODUCTION which the aim is to combine the throughput and power
In a cellular network user data is transmitted via base consumption advantages of the peer-to-peer model with the
station (BS) or other central network element when one user fairness, resilience and mobility advantages of the cellular
device is communicating with another user device. When model. [5]
communicating devices are relatively close to each other it Haas et al. provided system analysis results of frequency-
could be sensible to have a direct communication link instead division duplexing (FDD) wideband code division multiple
of conveying data via base station in order to save transmission access (WCDMA) cellular network where D2D communica-
power of both user devices and base stations, radio access as tion was enabled on uplink spectrum [2]. They concluded that
well as core network resources as discussed in [1]. The direct permitting D2D communication in time-division duplexing
communication mode requires half of the resources compared (TDD) mode at the cell edge results in a 1.5 times capacity
to cellular communication mode1 thus offering double spectral improvement over the scenario where only FDD cellular mode
efficiency per connection typically. Also if devices in direct operation is permitted. However the decision whether the
communication mode are close to each other transmission direct or cellular communication mode is selected for the
power levels could be lower than in cellular mode which user is based on comparing the path loss between device and
can be then turned into battery savings at the device and BS to a pre-defined path loss. If the pre-defined path loss
reduced interference levels in the system. Further, reduced is smaller, the direct mode is selected. Thus mode selection
wasn’t optimal in their studies because communication mode
1 Cellular communication mode means here a conventional radio access selection was made individually for one pair at the time
where a user device is having a communication links towards and from a BS without taking into account other users sharing the same
2 In WCDMA downlink based on UMTS standard physical channels are Fig. 1. Link gains between each device and BS, and between devices.
orthogonal in nature but channel dispersion makes channels non-orthogonal.
In uplink user devices are separated by non-orthogonal scrambling codes.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
Let’s assume that we have a cellular system where there are when transmission powers and communication modes are
both cellular communication mode and D2D mode devices selected properly. Similarly SINR for Device 2 is
sharing the radio resources of the UL band. Fig. 1 depicts
link gains3 between devices where devices 1 and 4 are both (t)
gc α2,b2 m2 p2
having a cellular communication link and device 2 and 3
(t) (t) (t)
≥ βc (2)
are having a D2D communication link with each other. In α1,b2 m1 p1 + α4,b2 (1 − m4 )a4 p4 + nb
addition, the figure illustrates the occasion when device 3 is
transmitting to device 2 in D2D mode. Let’s assume that we and SINR for Device 4 (in D2D connection mode) is targeted
have altogether L devices in the system. Further, we define a to be greater than or equal to βd as follows
local communication probability as plocal (D2D candidates).
Then there are f loor (plocal L) locally communicating devices (t) (t)
and ceil (f loor(plocal L)/2) candidate D2D pairs. For the gd γ4,3 (1 − m4 )a4 p4
(t) (t)
≥ βd (3)
derivation of the new system equations the following symbols γ1,3 m1 p1 + γ2,3 m2 p2 + nu
are used:
i, j User device indices with values 1 ≤ i, j ≤ L At the even time slot t SINR requirement for Device 1 is
m A communication mode selection vector, of
size L × 1, for devices (mi = 1 if device i
(t)
is in cellular mode and mi = 0 if device i gc α1,b1 m1 p1
(t) (t) (t)
≥ βc (4)
is in D2D mode) α2,b1 m2 p2 + α3,b1 (1 − m3 )a3 p3 + nb
a(t) A TDD activity vector (used only when
mi = 0), where for the odd time slot t (D2D
T SINR requirement for Device 2 is
using TDD) a(t) = 1 0 1 0 . . .
and
for the even time slot t a(t) =
T (t)
0 1 0 1 ... gc α2,b2 m2 p2
≥ βc (5)
βc A target signal-to-interference-and-noiser ra- (t)
α1,b2 m1 p1 + α3,b2 (1 − m3 )a3 p3 + nb
(t) (t)
tio (SINR) for cellular communication mode
physical radio link
βd A target SINR for D2D communication mode and SINR requirement for Device 3 (in D2D connection mode)
physical radio link
gc A processing gain for cellular communica- gd γ3,4 (1 − m3 )a3 p3
(t) (t)
for odd t and the element i in power vector has to be greater than zero.
(t) Equation (9) can also be formulated like in [12]
p⎛
i = mi ⎞
L βc αj,bi (t) P(t) = (t) P(t) + ℵ(t) (13)
⎜ mj p ⎟
⎜ j=1 gc αi,bi j ⎟
⎜ j=i ⎟ or
⎜ ⎟
⎜ L
(t) βc αj,bi (t) ⎟
·⎜ + (1 − mj ) aj pj ⎟
⎜ gc αi,bi ⎟
⎜ j=1 ⎟ (I − (t) )P(t) = ℵ(t) (14)
⎜ j=i ⎟
⎝ βc ⎠
+ nb where the interference matrix is
gc αi,bi
(t) (8)
+⎛(1 − mi ) ai ⎞
L βd γj,i−1 (t) (t) = M(ΦM + ΦA(t) − ΦMA(t) )
⎜ mj p ⎟ (15)
⎜ j=1 Gd γi,i−1 j ⎟ +A(t) (I − M)(ΘM + ΘA(t) − ΘMA(t) )
⎜ j=i ⎟
⎜ ⎟
⎜ L
(t) βd γj,i−1 (t) ⎟ and the noise vector
·⎜ + (1 − mj ) aj pj ⎟
⎜ gd γi,i−1 ⎟
⎜ j=1 ⎟
⎜ j=i ⎟ ℵ = MCNb + A(t) (I − M)Nu (16)
⎝ βd ⎠
+ nu
gd γi,i−1 The set of feasible power vectors under mode selection m
for even t. is
From (7) and (8) we can make a matrix form as follows: P(t) = P(t) ≥ 0 P(t) ≥ P(t) + ℵ (17)
⎛ ⎞
M
⎜ · ΦM + ΦA(t) − ΦMA(t) ⎟ (t) The set P(t) describes a cone of feasible powers in that
P(t) = ⎜
⎝ +A(t) (I − M)
⎟P
⎠ if p ∈ P(t) then αp ∈ P(t) for all α ≥ 1. Each cone P(t)
(9)
is specified by an interference matrix and noise vector ℵ.
· ΘM + ΘA(t) − ΘMA(t)
The non-negative noise vector displaces these cones from the
+MCNb + A(t) (I − M) DNu
origin. [6] On the other hand, one of the devices of D2D pair
where diagonal
C, of size L×L, has diagonal elements
matrix has power equal to zero due TDD duplexity depending on the
Cii = βc gc αi,b(i) , D, of size L×L, has diagonal elements on-going time slot. Since elements of M,Φ ,Θ and A are in
Dii = [βd /(gd γi,i+1 ) βd /(gd γi,i−1 ) . . . the range [0, 1], is non-negative. Thus Perron-Frobenius theory
(10) guarantees the existence of a dominant, positive eigenvalue r
βd /(gd γL−1,L ) βd /(gd γL,L−1 )], [13]. Equation (18) has a positive solution if and only if r < 1.
diagonal matrix A(t) has diagonal elements formed by a(t) , This is referred later as eigenvalue criteria. If r < 1 then there
diagonal matrix M formed from mode selection vector of is a unique solution P(t) given by
devices m, matrix Φ, of size L × L, defines gains against −1
interference from other devices when device in question is in P(t) = I − (t) ℵ(t) (18)
cellular communication mode and it has been formulated as
follows: ⎧ C. Utilization of System Equations
⎨ 0 i=j
Φij = βc αj,bi (11) Using (15) we can find the optimal mode selection vector
⎩ i = j m∗ for example via minimizing the first norm of power vector
gc αi,bi
combined from two consecutive time slots
matrix Θ, of size L × L, defines gains against interference
from other devices when device in question is in D2D com- arg min P(t−1) + P(t) (19)
M 1
munication mode and it has been formulated as follows:
⎧ subject to
⎪ 0 i=j
⎪
⎪ −1 (t)
⎨ βd γj,i+1
i = j, i is odd P(t) = I − (t) ℵ
Θij = gd γi,i+1 (12)
⎪
⎪ βd γj,i−1
(t) (t)
pi = 0 : mi = 0, ai = 0
⎪
⎩ i = j, i is even, (t) (t)
gd γi,i−1 pi > 0 : mi = 1 OR mi = 0, ai = 1
vector
Nb , of size L × 1, is defined as follows: Nb = Further one can find a probability for having a dominant
T
nb nb · · · nb , vector Nu , of size L × 1, is defined positive eigenvalue of the interference matrix (14) that is
T
as follows: Nu = nu nu · · · nu , and A(t) is a less than unity. Then we can analyse system capacities as
diagonal matrix formed from a vector a(t) . a function of system outage when D2D is allowed using an
For P(t) we have to have a non-negative vector where the optimal mode selection and compare those results to the pure
element i can be zero only if mi = 0 and ai = 0. Otherwise cellular mode system and practical mode selection algorithms.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
TABLE I
S IMULATION PARAMETERS FORCE D2D D2D mode is selected always for locally
communicating devices.
Parameter Value
To study capacity in a cellular network we are mainly
Cellular layout Isolated cell, 1-sector
interested in to find the capacity when the system outage is
System area User devices are distributed within
a range of 500 m from the BS
around 5 %. The system outage here is referred to a probability
Path loss model for cellular link 128.1 + 37.6log10(d[km]) [14]
that eigenvalue criteria of the interference matrix (14) cannot
Path loss model for D2D link 148 + 40log10(d[km]) [14]
be fulfilled. We simulate the system realization via means
of multiple independent drops and by averaging over the
Shadow fading standard deviation 10 dB for cellular mode links and
12 dB for D2D mode links [14] drops we can derive the probability for the eigenvalue criteria
Noise spectral density -174 dBm/Hz with certain parameter settings. The obtained probability is
System bandwidth 5 MHz considered as the system outage.
Noise figure 5 dB at BS / 9 dB at device In Fig. 2 one can obtain the system capacity in terms of the
Minimum coupling loss 70 dB BS-Device / 40 dB Device- number of users in the system for the outage probability being
Device 5 % when maximum distance between locally communicating
Antenna gains and patterns (trans- BS: 14 dBi Device: Omnidirec- devices is 50 metres and local communication probability is
mitter and receiver) tional 0 dBi
either 0.2 or 0.4. It can be seen that when the maximum D2D
Processing gain Cellular 30 / D2D 15
distance is quite large there is not much potential improvement
Probability of local communication 0.2, 0.4 available from D2D capability in the system. The available
per device
performance improvement increases as a function of increasing
Maximum distance between locally 5, 50 [m]
communicating devices local communication probability. On the other we can see
how dangerous it would be to use path loss based or forcing
all locally communicating devices into D2D communication
IV. P ERFORMANCE ANALYSIS mode in this case. Those methods really deteriorate the system
In this section system level simulations are carried out using performance and actually as local communication probability
previously generated system equations to find out optimum increases the situation goes even worse. This is due to fact
and practical capacities of the system when D2D is allowed. that these methods don’t consider the interference situation at
The results are compared to pure cellular communication mode all.
case.
System capacity at 5th percentile, 50 m
A. Simulation Model, User Distribution and Simulation Pa- 80
rameters CELLULAR
OPT D2D
The network consists of one BS with one sector. Probability 70
PL D2D
for locally communicating devices is given as a simulation
System capacity at 5th percentile
FORCE D2D
parameter per device. Devices that don’t have a local commu- 60
nicating peer are distributed uniformly over the system area.
Two consecutive devices that are having a local communica- 50
tion in terms of devices indices form a pair. One device of
the pair is distributed uniformly over the system area whereas 40
the other device of the pair is distributed uniformly upon a
disk centered by the first device and radius of the disk is 30
given as a simulation parameter. Thus the radius gives the
20
maximum distance between locally communicating devices.
Used simulation parameters are provided in Table I.
10
B. Simulations (Numerical Analysis)
Here we analyse system capacities against system outage in 0
p_local 0.2 p_local 0.4
four different cases:
CELLULAR All devices are in cellular mode (no D2D Fig. 2. System capacity at 5th percentile of the system outage when
communication mode available). maximum D2D distance is 50 m and local communication probabilities are
0.2 and 0.4 for different mode selection algorithms compared to pure cellular
OPT D2D Mode selection vector for all devices is communication mode system.
searched in order to minimize the first norm
of the device powers combined over two time
slots (18) and to fulfill eigenvalue criteria. Impact of decreasing the maximum distance between locally
PL D2D D2D mode is selected if path loss between communicating devices can be seen in Fig. 3 where the
communicating devices is less than minimum maximum distance is 5 metres. Now we can see that even path
of path losses between each device and BS. loss based and forcing D2D methods behave quite well, almost
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2010 proceedings.
reaching the achievable upper bound. In addition to gains probability and maximum distance between communicating
with optimal mode selection method, gains with two other devices, as well as mode selection algorithm.
mode selection methods increase as the local communication In the future, interference-aware mode selection algorithm
probability increases. could be evaluated against above mentioned mode selection
From above observations one could think a practical mode algorithms to find a practical algorithm to achieve close
selection algorithm to be such that it could first check if the to optimum gains from D2D also when maximum distance
path loss or link gain between locally communicating devices between communicating devices increases. Also, one could use
were below a certain threshold. The algorithm could then different deployment scenarios to analyse D2D performance,
further use above described path loss based mode selection for example in indoor environments.
criteria (PL D2D) to decide the used communication mode for
R EFERENCES
the D2D pair in question. On the other hand, in the system
where devices share the same radio resource, the practical [1] J. Lehtomäki, I. Suliman, J. Vartiainen, M. Bennis, A. Taparugssanagorn,
and K. Umebayashi, “Direct communication between terminals in infras-
mode selection algorithm could be based on interference- tructure based networks,” in Proceedings of the ICT Mobile and Wireless
awareness in which interference measurements from devices Communications Summit, Stockholm, Sweden, 2008.
could be used for mode selection especially in the case of the [2] P. E. Omiyi and H. Haas, “Maximising spectral efficiency in 3G with
hybrid ad-hoc UTRA TDD/UTRA FDD cellular mobile communica-
large maximum distance between communicating devices. tions,” in Proceedings of the IEEE International Symposium on Spread
Spectrum Techniques and Applications, Sydney, Australia, Sep. 2004,
pp. 613–617.
System capacity at 5th percentile, 5 m [3] Y. Zhang, L. Du, D. Shang, and Y. Yang, “Performance analysis of a
80 p2p-enabled tdd-cdma network with intra-cell spatial resource reuse,”
CELLULAR Wirel. Commun. Mob. Comput., vol. 9, no. 8, pp. 1059–1069, 2009.
70 OPT D2D [4] H.-Y. Hsieh and R. Sivakumar, “On using peer-to-peer communication
PL D2D in cellular wireless data networks,” IEEE Transactions on Mobile
System capacity at 5th percentile