1 11 subcarrier allocation and bit loading algorithms for ofdma-based wireless networks gautam...
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111
Subcarrier Allocation and Bit Loading Algorithms for OFDMA-Based Wireless
Networks
Gautam Kulkarni, Sachin Adlakha, Mani Srivastava
UCLAIEEE Transactions on
Mobile Computing 2005
222
Outline
Introduction System Model and Problem Formulation Centralized Rate Allocation Algorithms Distributed Algorithm Performance Evaluation Conclusions
3
OFDM
Frequency Division Multiplexing (FDM)
Orthogonal Frequency Division Multiplexing (OFDM) higher spectral efficiency
4
OFDMA
Orthogonal Frequency Division Multiple Access (OFDMA) the sub-carriers are divided into groups of sub-carriers
Each group is named a sub-channel sub-channels can be allocated to users depending on
their channel conditions and data requirements different transmit power and modulation
5
Goal
We address the problem of subcarrier, bit, and power assignment for networks that employ OFDMA
Our objective is to minimize the total transmitted power over all links while maintaining the data rates on each link
6
System Model
There are a total of M links in the network, each with a certain data rate requirement Ri
Let the spectrum of interest be divided into N subcarriers Pc
i is the power transmitted by transmitter i on subcarrier c
Ici is the interference power
Let Gcij be the gain from the transmitter of link j to the
receiver of link i for subcarrier c The SINR of link i for subcarrier c is given by
7
SINR Threshold Let bc
i be the number of bits transmitted by link i on subcarrier c bc
i takes only integer values ∈(0, 1, 2, ..., bmax), where bmax is the maximum modulation level used
When M-ary quadrature amplitude modulation (M-QAM) [13] is used, the corresponding SINR threshold is ex: 16-QAM, 64-QAM
where BER is the target bit error rate and Q(.) is the Gaussian tail function given by
[13] J.G. Proakis, Digital Communications. McGraw Hill, 2001
8
Matrix Form
The data rate Ri can be expressed as
When K links (i1, i2, ..., iK) are transmitting on subcarrier c, we require that
In matrix form, these conditions can be written as
Where
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Example
(D)
(C))(
(B)
(A)
1
1
1
13
2,11
1,1
3,132,121111,1
1,1
113
1,1
3,112
1,1
2,111
3,3
33
2,2
22
1,1
11
3
2
1
3,3
2,33
3,3
1,33
2,2
3,22
2,2
1,22
1,1
3,11
1,1
2,11
rGPN
PG
GPGPNrPG
G
NrP
G
GrP
G
GrP
G
Nr
G
Nr
G
Nr
P
P
P
G
Gr
G
Gr
G
Gr
G
Gr
G
Gr
G
Gr
iii
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Pci is a function of {bc
i}
It was shown in [14] that a positive solution for Pc exists if the maximum eigenvalue of Fc is less than 1 Otherwise, the set of SINR thresholds (modulation levels) used by all
the links on subcarrier c, is not feasible The goal is to find bc
i and Pci for every link i and subcarrier c
(the Pareto optimal solution)
ccc UFIP 1)(
[14] J. Zander, “Performance of Optimum Transmitter Power Controlin Cellular Radio Systems,” IEEE Trans. Vehicular Technology,vol. 41, no. 1, pp. 57-62, Feb. 1992.
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Problem Formulation
Finding the global minimum requires an exhaustive search over all possible assignments of subcarriers to links
12
Let P(i, c, b△ ci) be the total
increase in transmitter power over all links when one more bit of link i is
loaded on subcarrier c
14
Graph-Based Approach We adopt the strategy of using small modulation levels and spreading
the data rate over a large number of channels This would imply smaller power levels per channel and higher spatial
reuse
Procedure Step 1. Construct the interference graphs Hc = (V , Ec) for all c ∈ 1,
2, ..., N Step 2. Start with c = 1 Step 3. Find a maximal independent set of Hc using the Minimum
Degree Greedy Algorithm [25] Step 4. From the maximal set, find a feasible set of transmissions (S) Step 5. Trim the interference graphs for all channels by removing S Step 6. Proceed to next channel—stop if all channels scheduled or all
sublinks are scheduled
15
Distributed Algorithm (1)
In this case, node have no knowledge of channel gains for the entire network
Time is divided into slots and every link updates its power at the end of each slot as follows
Pci(k) is the power transmitted by link i on subcarrier c in time
slot k γc
i is the measured SINR at the receiver of link i It was shown in [14] that the power update (11)
converges to the Pareto optimal[14] J. Zander, “Performance of Optimum Transmitter Power Controlin Cellular Radio Systems,” IEEE Trans. Vehicular Technology,vol. 41, no. 1, pp. 57-62, Feb. 1992.
r
r
kP
kP
)(
)1(
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Distributed Algorithm (2)
A link selects a particular subcarrier and loads one bit and then performs power control to try to achieve the corresponding SINR threshold The criterion for selecting the subcarrier is the Gc
i/Ici factor
the subcarrier with the highest Gci/Ic
i factor is selected
Gci and Ic
i are the channel gain and interference, respectively
After a few power control updates (W slots), the power transmitted by the link on the selected subcarrier may not stabilize and is still increasing Each link i drops out with a probability q(i) The probability q(i) is increased with each unsuccessful attempt to
gain access to the channel
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Comparison with the Optimal Solution
The performance of our algorithms vs. the optimal solution for small instances of the problem the two link, two channel case
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Simulation Environment
10 links in an area of 200 m by 200 m Receivers are randomly placed within a 20 m
radius of the corresponding transmitter 48 subcarriers in the OFDM system The path loss exponent is taken to be 4 bit rate requirements of the links are normal
random variables For the distributed algorithm, we choose W = 10
slots and qthresh = 0.95
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Conclusions
Consider the problem of subcarrier and bit allocation for point-to-point links of fixed wireless networks without base stations The objective was to minimize the total transmitted
power over all links while trying to satisfy the data rate requirement of each link
Present centralized and distributed heuristic algorithms for allocating rates to the links