1 Introduction
2 Related work
3 System overview
3.1 Directional MAC structure
3.2 Transmission model
3.2.1 Antenna model
3.2.2 Channel model
3.3 Interference level
-
Case 1: \({l_{i}^{x}}\) does not exist in reality, i.e., t i =r i .
-
Case 2: \({l_{i}^{x}} = {l_{j}^{y}}\), which means that i=j,x=y. \(l_{i}^{x}\) and \(l_{j}^{y}\) are the same tuple link.
-
Case 3: \({l_{i}^{x}} \ne {l_{j}^{y}}\), which means that \(l_{i}^{x}\) and \(l_{j}^{y}\) are different tuple links. They operate on a diverse channel with disparate radios.
-
Case 4: \({l_{i}^{x}} \ne {l_{j}^{y}}\), they share the same radio.
-
Case 5: \({l_{i}^{x}} \ne {l_{j}^{y}}\), they have the common node(s) and operate on the same channel with disparate radios. The common node(s) transmit and receive simultaneously [15].
3.4 Problem overview
4 Problem formulation
Symbol | Description |
---|---|
K
| The number of pairings in a schedule |
V
| The number of flows in the network |
M
v
| The number of paths of the v-th flow |
H
vp
| The number of hops of the p-th path of the v-th flow |
d
v
| The traffic demand of the v-th flow |
d
vp
| The traffic demand distributed to the p-th path |
l
vpi
| The i-th link of the p-th path of the v-th flow |
c
vpi
| The transmission rate of link l
vpi
|
L
uqj
| The set of tuple links of link l
vpi
|
\({l_{vpi}^{x}}\)
| The x-th tuple link of link l
vpi
|
t
vpi
| The transmitter of link l
vpi
(tuple link \({l_{vpi}^{x}}\)) |
r
vpi
| The receiver of link l
vpi
(tuple link \({l_{vpi}^{x}}\)) |
\(a_{vpi}^{k}\)
| A binary variable to indicate whether link l
vpi
is scheduled in the k-th pairing |
\(a_{vpi}^{xk}\)
| A binary variable to indicate whether tuple link \({l_{vpi}^{x}}\) is scheduled in the k-th pairing |
\(\textbf {R}_{{t_{pi}}}\)
| The set of radios of node t
vpi
|
C
| The set of channels in the network |
\({W_{vpi,uqj}^{x,y}}\)
| The interference level of tuple link \({l_{vpi}^{x}}\) caused by \({l_{uqj}^{y}}\) |
4.1 Problem formulation and analysis
-
Constraint (10) indicates regular flow restriction.
-
Constraints (16)–(18) represent scheduling restrictions. Constraint (16) indicates the inherent order of transmission in each path, the (i+1)-th link of the p-th path of the v-th flow should be scheduled after the i-th link. Constraints (17)–(18) indicate SINR restriction for concurrent transmissions.
4.2 Problem reformulation
4.3 Example
5 The MPMH-MRMC scheme
Symbol | Description |
---|---|
R
0
| The number of radios of a node in the network |
N
| The number of nodes |
P
s
| Set of selected paths of all flows |
H
| Set of links in P
s
|
l
pi
| The i-th link of the p-th path |
\({l_{pi}^{x}}\)
| The x-th tuple link of link l
pi
|
w
pi
| The initial weight of link l
pi
|
\({w_{pi}^{t}}\)
| The remaining weight of link l
pi
in the t-th pairing |
t
pi
| The transmitter of link l
pi
(tuple link \({l_{pi}^{x}}\)) |
r
pi
| The receiver of link l
pi
(tuple link \({l_{pi}^{x}}\)) |
\(\textbf {R}_{{t_{pi}}}^{t}\)
| Set of unused radios of transmitter t
pi
in the t-th pairing |
\(\textbf {R}_{{r_{pi}}}^{t}\)
| Set of unused radios of receiver r
pi
in the t-th pairing |
F
p
| The hop number of the first unscheduled link of the p-th path |
\({\textbf {P}_{muh}^{t}}\)
| Set of unvisited paths with the largest number of unscheduled links |
\(\textbf {P}_{u}^{t}\)
| Set of unvisited paths in the t-th pairing |
H
t
| Set of links in the t-th pairing |
\(\textbf {H}_{0}^{t}\)
| Set of tuple links in the t-th pairing |
δ
t
| Number of time slots of the t-th pairing |
\({I_{pi}^{x}}\)
| The cumulative interference level of tuple link \({l_{pi}^{x}}\) |
5.1 Symbols in MPMH-MRMC scheme
5.2 Working mechanism of MPMH-MRMC scheme
5.3 Example
6 Simulation results
6.1 Simulation setup
Symbol | Description | Value |
---|---|---|
W
| Channel bandwidth | 1200 MHz |
P
t
| Transmission power | 0.1 mW |
N
0
| Background noise | −114 dBm/MHz |
ρ
| Path loss exponent | 2 |
A
LOS
| LOS path loss constant | 32.5 dB |
θ
−3 dB
| The antennas HPBW | 60° |
T
slot
| Slot duration | 5 μs |