Video quality-rate model in Chapter 2.3 is employed. Based on the above throughput analysis of all four modes, in this section, we develop resource allocation strategies
that maximize the quality of the received video at D2 under certain constraints. Both
bandwidth allocation and transmit power level Pd at D1 are optimized.
5.3.1
Cellular Mode
In cellular mode, the video quality maximization problem is formulated as max B,Pd QD = aDln(RD) + bD (5.25) subject to Bc1+ Bc2+ Bd1+ Bd2 ≤ B (5.26) QC ≥ Qcmin (5.27) Pd ≤ Pdmax (5.28) RD Pci+Pd ≥ ηd (5.29)
Above, (5.29) defines the EE constraint at D1. Energy efficiency (EE), measured
by the data rate normalized by the transmission power or equivalently the number of communicated bits per unit energy, is also considered as a key factor in wireless systems. ηd is the minimum EE requirement. Since QC is an increasing function of
ˆ
Bc1, the minimum required bandwidth ˆBc1min allocated to cellular uplink C1− BS
is the solution of (5.27) with equality. Then, there is a unique Bcmin = Bcmin1 that
satisfies (5.8) and there is another unique Bcmin = Bcmin2 satisfying the equality in
(5.9) depending on the value of θ. It is easy to verify that the maximum of these two values of Bcmin needs to be chosen as the minimum bandwidth allocated to the
cellular link. Thus, Bcmin = max{Bcmin1, Bcmin2}. Then, the rest of the bandwidth
Bd = B −Bcminis allocated to the D1−BS −D2 link since larger bandwidth allocated
to the D2D link leads to higher throughput and furthermore higher PSNR value for the received video at D2. The EE constraint (5.29) can be rewritten as
RD ≥ ηd(Pci+
Pd
by moving the denominator to the right-hand side. It can be easily shown that the left-hand side of (5.30) is an increasing concave function, and the right-hand side of (5.30) is a linear increasing function of Pd for given Bd1 = Bd1a with initial points at
(0, 0) and (0, ηdPci), respectively. By fixing Bd1, we consider both sides of (5.30) as
functions of Pd, and the left-hand side of (5.30) will intersect the right-hand side of
(5.30) at two different points, the minimum available or required power, Pdmin1, and
the maximum again available or required power, Pdmax1 when Bd1 is large enough.
There is no solution for the optimization problem if Bd1 is small, since (5.30) cannot
be satisfied for any value of Pd. Therefore, the transmission power at D1 needs to
be in the range Pdmin1 ≤ Pd ≤ Pdmax1 in order to satisfy the EE constraint. Since
the left-hand side of (5.30) is also an increasing function of Bd1 but the right-hand
side is independent of Bd1, larger Bd1 leads to larger Pdmax1 and smaller Pdmin1.
Therefore, larger bandwidth Bd1 allocated to the uplink of D2D link will lead to
larger maximum feasible power Pdmax1 and smaller minimum feasible power Pdmin1
under the EE constraint. In another words, increasing Bd1 enlarges the region of
Algorithm 3 Resource allocation for the cellular mode
1: Determine the minimum throughput of the cellular link, Rcmin by solving (5.27)
with equality.
2: The minimum bandwidth, ˆBc1min allocated to cellular uplink is obtained by solv-
ing (5.7).
3: Let ˜Bc1 = ˆBc1min. Then, the minimum bandwidth, Bc = Bcmin1 is the solution
of (5.8). And let Bc1∗ = ˆBc1min. Then, Bc = Bcmin2 is the solution of (5.9).
Bcmin = max{Bcmin1, Bcmin2} is chosen as the minimum bandwidth allocated to
the cellular link. This satisfies the minimum required quality of the received video at C2, and Bd= B − Bcmin is allocated to the D1− BS − D2 link.
4: As initialization, assume that Bd1 = B0 is allocated to the D1 − BS link and
Bd2 = Bd− Bd1 is allocated to the BS − D2 link. Pdmin1 and Pdmax1 are the
minimum and maximum feasible transmission power levels of D1 limited by the
two-hop link throughput constraints (5.11) and (5.12), respectively. Pdmin2 and
Pdmax2 are the minimum and maximum feasible transmission power levels of D1
limited by EE constraint (5.30). Let Pdmax1 = Pdmax, Pdmax2 = 0, p = 0.0001
and α = 0.001.
5: while |Pdmax1− Pdmax2| > p and Bd1 <= Bd do
6: Let ˆBd1 = Bd1, and obtain Pdmin1 and Pdmax1 by solving (5.30) with equality,
and obtain Pdmin2 and Pdmax2 by solving (5.11) and (5.12) as discussed above.
7: Update Bd1 = Bd1+ α(Pdmax2− Pdmax1)
8: end while
9: if Bd1> Bd then
10: No solution. 11: else
12: Pd= min{Pdmax2, Pdmax1} and ˆBd1= Bd1. Quality of the received video at D2,
QD, is obtained by calculating (5.10) and (??).
Also, for fixed Bd1, Pdmax2a is determined by (5.11) and Pdmax2b is determined by
(5.12). It is easy to verify that the minimum one should be chosen as the transmission power at D1, and hence we assume that Pdmax2 = min{Pdmax2a, Pdmax2b}. Therefore,
the transmission power at D1 should satisfy 0 ≤ Pd ≤ Pdmax2 for the two-hop link
in cellular mode. For this fixed Pdmax2, the left-hand sides of (5.11) and (5.12) are
increasing functions of Bd1, and the right-hand sides are decreasing functions of Bd1.
A bandwidth larger than Bd1 cannot be allocated to D2D uplink under this fixed
transmission power Pdmax2. However, left-hand sides of (5.11) and (5.12) are increas-
ing functions of Pd, therefore, lower Pdmax2 can satisfy the two-hop link throughput
when Bd1 increases. In another words, increasing Bd1 shrinks the region of feasible
levels of the transmission power, Pd and decreases the throughput of this two-hop
link.
Therefore, we can decrease Bd1 if Pdmax2 < Pdmax1, or otherwise, we increase
Bd1 until we satisfy Pdmax1 = Pdmax2 since the quality of the received video at D2
is determined by Bd1 and min{Pdmax1, Pdmax2}. The detailed algorithm of resource
allocation for the cellular mode is explained in Algorithm. 3.
5.3.2
Dedicated Mode
In dedicated mode, since a separate bandwidth of Bd is allocated to the D2D direct
link, the minimum bandwidth, Bcmin, allocated to the cellular link is obtained sim-
ilarly as in cellular mode. Therefore, Bd = B − Bcmin is allocated to the D2D link
and the maximum transmission power Pdmax can be obtained by using (5.14) and
satisfying the EE constraint RD
Pci+Pdmax
≥ ηd with equality. QD reaches the maximum
value at (Bd, Pdmax) since Pdmaxis an increasing function of Bdas discussed in cellular
5.3.3
Reuse Modes
In reuse modes, we seek to maximize the QD by allocating the bandwidths Bc1, Bc2
and choosing the transmission power Pdat D1optimally in the presence of interference
constraints in the system. The optimization problem is formulated as max B,Pd QD = aDln(RD) + bD (5.31) subject to Bc1+ Bc2 ≤ B (5.32) QC ≥ Qcmin (5.33) Pd≤ Pdmax (5.34) RD Pci+Pd ≥ ηd (5.35)
In uplink reuse mode, QC depends on Bc1 and Pd due to the interference from D1.
Let us substitute (5.15) and (5.16) into (5.8) and (5.9). Let us set Bc1 and Pdmin1 as
the bandwidth allocated to the C1 − BS link and corresponding minimum feasible
transmission power at D1, which achieves the maximum throughput in the cellu-
lar link. When Bc1 increases, the right-hand sides of both (5.8) and (5.9) decrease
because Bc2 = B − Bc1 decreases. In order to satisfy (5.8) and (5.9) with equal-
ity, Pdmin1 has to be increased since left-hand sides of (5.8) and (5.9) are decreasing
functions on Pd. Therefore, increasing Bc1 leads to increased Pdmin1 and decreased
throughput in the cellular link. Letting Pd = Pdmax and Pd = 0, we can obtain the
corresponding maximum bandwidth Bc1max and the minimum bandwidth Bc1min, re-
spectively. Similarly as we discussed in cellular mode, decreasing Bc1 leads to smaller
region of feasible levels of transmission power Pd, indicating an increased minimum
power Pdmin2 and decreased maximum power Pdmax2 under the EE constraint. Since
QD depends on Bc1 and Pd due to presence of the interference, we cannot deter-
For a given Bc1, the maximum power Pdmax3 is obtained by satisfying (5.33) with
equality since QC is a decreasing function of Pd. Therefore, the minimum transmis-
sion power is Pdmint = max{Pdmin1, Pdmin2} and the maximum transmission power is
Pdmaxt = min{Pdmax2, Pdmax3}. Since Pd = Pdmax is the only power value that can
be used when Bc1 = Bc1max, the optimal solution is (Pd, Bc1) = (Pdmax, Bc1max)
if Pdmax2 = Pdmax3 = Pdmax is also achieved when Bc1 = Bc1max. Otherwise,
Pdmaxt < Pdmin1 when Bc1 = Bc1max. Since QD is an increasing function of Bc1
and Pdmaxt and decreasing Bc1 leads to reduced Pdmin1 and Pdmaxt, the first point of
Pd = Pdmin1= Pdmaxt achieved by decreasing Bc1 from Bc1max is the optimal solution.
Algorithm 4 Resource allocation for the uplink reuse mode
1: Substitute (5.15) and (5.16) into (5.8) and (5.9) and obtain the maximum feasible bandwidth Bc1max and minimum bandwidth Bc1min by setting Pd = Pdmax and
Pd = 0, respectively. Another minimum bandwidth value, Bc1min2 can be found
by solving (5.33) with the equality and setting Pd = 0.
2: Initialize that Bc1max∗ = Bc1max, Bc1min∗ = max{Bc1min, Bc1min2}, Bc1 = Bc1max,
p = 0.0001, α = 0.001, Pdmaxt = 0 and Pdmin1 = Pdmax.
3: while |Pdmaxt− Pdmin1| > p and Bc1> Bc1min∗ do
4: Find Pdmin1 by letting CUs satisfy two-hop link conditions (5.8) and (5.9) as
discussed in cellular mode. Obtain the minimum power Pdmin2 and maximum
power Pdmax2 by solving the EE constraint (5.35) with equality. Determining
the maximum power Pdmax3 by satisfying minimum quality requirement (5.33)
with equality.
5: Let Pdmaxt = min{Pdmax2, Pdmax3}.
6: Update Bc1 = Bc1+ α(Pdmaxt− Pdmin1).
7: end while
8: if Bc1< Bc1min∗ then
9: No solution.
10: else
11: Maximum QD is achieved at (Bc1, min{Pdmaxt, Pdmin1})
12: end if
In downlink reuse mode, the minimum bandwidth Bc1min allocated to the cellular
uplink is obtained by satisfying the minimum quality requirement (5.33) with equality since there is no interference term in RD. Thus, a bandwidth of Bd= B − Bc1min is
allocated to the cellular downlink and the D2D link. For given ˆBc1= Bc1min, Pdmax1is
obtained by solving (5.8) with equality. Pdmax2is obtained by solving (5.9) with equal-
the maximum transmission power at D1, i.e., Pdmaxt = min{Pdmax1, Pdmax2}. Similarly
as in uplink reuse mode, for a given Bd, Pdmin3 and Pdmax3 are determined by satis-
fying the EE constraint (5.35) with equality. Therefore, Pd= min{Pdmaxt, Pdmax3} is
the optimal transmission power that leads to maximum QD.
5.4
Numerical Results
In this section, we perform comprehensive simulations to evaluate the performance of video transmissions by the DUs in the D2D underlaid cellular networks.
5.4.1
Simulation Settings
It is assumed that the noise variance of each link is N0 = 0.01. Let ddd, ddb, dbd,
dcd, dcb, dbc and ddc denote the distances between D1 and D2, D1 and BS, BS
and D2, C1 and D2, C1 and BS, BS and C2, and D1 and C2, respectively. Unless
mentioned explicitly, we also assume that the channel power gains, denoted by z, follows exponential distributions with mean Z = 3d14, where d denotes distance. The
maximum transmission powers are Pdmax = 10 dB at D1, Pc = 10 dB at C1 and
Pb = 20 dB at the BS. Total bandwidth B = 2 MHz, EE coefficient ηd is set to
5 × 104, and the circuit power is P
ci = 0.1. PSNR is chosen as the performance metric
to measure the quality of the received video and the minimum required quality of the received video at C2 is 30 dB. Channel coherence time is set to 0.01.
5.4.2
Simulation Results
Fig. 5.2a - Fig. 5.2d show the PSNR values QD in four different modes as we vary the
location of D1 while keeping the locations of other nodes the same. In Fig. 5.2a, D1
whose location is closer to the BS has a higher QD value since there is no interference
between D2 and BS the same, and the link D1 − BS has better channel quality or
higher channel gain when D1 is closer to BS. Fig. 5.2b shows that the direct D2D
link has better performance when the distance between D1 and D2 is smaller due to
the larger channel gain. In Fig. 5.2c, not all the constraints can be satisfied in the region close to BS due to the strong interference from D1 at BS and also in the region
far away from D2 due to worsened channel quality. The region in which D1 is closer
to D2 has higher quality of the received video. We have similar observations in Fig.
5.2d, but different from the uplink reuse mode, there is no convex region near BS since D2D link shares the cellular downlink spectrum and C2is far away from D1. Fig. 5.2e
is the color-coded plot of optimal model selection results among four different modes, depending on the location of D1. We notice that uplink reuse mode is selected in the
region that is closest to the BS due to C1 and D1 being relatively far away from D2
and BS, respectively, and the interferences between these two links are small enough and more bandwidth being allocated results in higher video quality. Dedicated mode is selected in the yellow region, since D1 is close enough to D2 and this mode has
better performance compared to the cellular mode. The dedicated mode is also better than uplink reuse mode since the channel gain between D1 and D2 is getting smaller
and the impact of interference is starting to dominate the performance in uplink reuse mode. Cellular mode is selected in the light blue region since the channel gain of direct D2D link is worse than what is experienced in the two-hop link. Downlink reuse mode is not selected since the interference at D2 caused by BS is larger than the interference
at BS caused by D1 while the distance between D1 and D2 is small, and any other
mode is selected when D1 is far away from D2. And in the dark blue region, not
all the constraints can be satisfied. Fig. 5.2f demonstrates the corresponding PSNR values of the received video with the optimally selected modes.
Fig. 5.3a - Fig. 5.3d show the PSNR values QD for four different modes as we
−3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 BS D2 C 1 C2 0 5 10 15 20 25 30 35
(a) Cellular mode
−3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 BS D2 C 1 C2 0 5 10 15 20 25 30 35 40 45 (b) Dedicated mode −3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 BS D2 C1 C 2 0 5 10 15 20 25 30 35 40 45
(c) Uplink reuse mode
−3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 BS D2 C1 C 2 0 5 10 15 20 25 30 35 40 45
(d) Downlink reuse mode
−3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 BS D2 C1 C 2 NA Cellular Dedicated Uplink reuse
(e) Mode selection
−3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 BS D2 C1 C 2 0 5 10 15 20 25 30 35 40 45 (f) Corresponding QD values
Figure 5.2: QD values for different locations of D1 for (a) cellular mode; (b) dedicated
mode; (c) uplink reuse mode and (d) downlink reuse mode; (e) the optimal mode selection and (f) the corresponding QD values
Fig. 5.3a, D2 whose location is closer to the BS receives video with higher quality
QD since there is no interference in cellular mode, D1 transmits data to D2 though
the BS while the distance between D1 and BS is being kept the same, and the link
BS − D2 has better channel quality or higher channel gain when D2 is closer to BS.
Since the distance between D1 and BS is fixed and close enough, all constraints are
satisfied in almost the entire region, which is not the case when the location off D1
was varied. Fig. 5.3b shows that the direct D2D link has better performance when the distance between D1 and D2 is smaller due to same reason as discussed when D1
was being moved. In Fig. 5.3c, unlike the case of D1 being moved, there is no convex
region when D2 is closer to the BS since there is no interference between D2 and BS.
The region in which D2 is closer to D1 has higher quality of received video. This is
similar to the observation in Fig. 5.3c. The region in which D2 is closer to D1 has
higher received video quality in Fig. 5.3d, but different from the uplink reuse mode, the upper boundary of the lower (yellow) region is flat due to D2 being closer to BS,
−3 −2 −1 0 1 2 3 −3 −2 −1 0 1 2 3 BS D1 C 1 C2 30.9 30.92 30.94 30.96 30.98 31 31.02 31.04 31.06 31.08
(a) Cellular mode
−3 −2 −1 0 1 2 3 −3 −2 −1 0