1 Introduction
1.1 Literature overview
1.2 Contributions
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A cooperative relaying model is proposed, where mobile users may serve as relays to other users, while still transmitting their own data to the BS.
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The corresponding RB and power allocation algorithm, aiming at minimizing the total consumed power, is determined using Lagrange dual decomposition.
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Two relay selection algorithms are proposed: a fixed relay selection strategy, where a source uses the same relay on all RB, and an adaptive strategy where relay selection is jointly optimized with resource allocation. In this case, a source may use different relays on different RB, and may also directly transmit to the BS on some other RB.
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The complexity and overhead of the two algorithm’s variants are evaluated, and several simulation results are provided to assess their performance.
2 System model and problem formulation
2.1 System model
2.2 Problem formulation
NRS | RS | R | |
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TTI 1 |
\( P_{NRS}^{(j)}\)
|
\( P_{RS}^{(j^{\prime })}\)
| 0 |
TTI 2 |
\( P_{NRS}^{(j)}\)
| 0 |
\(P_{R}^{(j^{\prime })}+P_{R}^{(j^{\prime \prime })}\)
|
Average Power per TTI |
\(P_{NRS}^{(j)}\)
|
\(\frac {1}{2} P_{RS}^{(j')}\)
|
\(\frac {1}{2} \left (P_{R}^{(j^{\prime })}+P_{R}^{(j^{\prime \prime })}\right)\)
|
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b =[b 1,b 2,....,b K ] T is the vector of users decisions of cooperation. b k =1 is k is a R or a RS, and b k =0 otherwise. Please note that in the joint relay selection strategy, a user is considered a RS if its data is relayed in at least one RB. Similarly, a user is considered a R if it relays some data in at least one RB.
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P is the power matrix per user in each RB:$$ \mathbf{P} = \left(\begin{array}{llll} P_{1}^{(1)} & P_{1}^{(2)}&....&P_{1}^{(N)}\\ P_{2}^{(1)} & P_{2}^{(2)}&....&P_{2}^{(N)}\\.&.&.&.\\.&.&.&.\\ P_{K}^{(1)} & P_{K}^{(2)}&....&P_{K}^{(N)} \end{array} \right) $$(4)
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a is the RB allocation matrix per couple of (source, relay) and each RB j:$$ \mathbf{a} = \left(\begin{array}{llllll} a_{1,1}^{(1)} &..& a_{1,K}^{(1)}& a_{1,1}^{(2)}&..&a_{1,K}^{(N)}\\ a_{2,1}^{(1)} &..& a_{2,K}^{(1)}& a_{2,1}^{(2)}&..&a_{2,K}^{(N)}\\.&.&.&.&.&.\\.&.&.&.&.&.\\ a_{K,1}^{(1)} &..& a_{K,K}^{(1)}& a_{K,1}^{(2)}&..&a_{K,K}^{(N)} \end{array} \right) $$(5)
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Constraint (3e) represents the cooperative decision for user k, b k =1 if user k is involved in a cooperative manner (k is a RS or a R), b k =0 otherwise.
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Constraints (3b) and (3d) represent the RB allocation constraints, \(a_{k,k}^{(j)} = 1\) means that RB j is assigned to the transmission of user k towards the BS. \(a_{k,r}^{(j)} = 1\) with k≠r means that RB j is assigned to the transmission of user k towards relay r in the first TTI and transmission of relayed data from r to BS in the second TTI. If there exists at least one subcarrier j such that \(a_{k,r}^{(j)} = 1\), then b k =1 and b r =1.
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Constraint (3f) ensures that all powers are positive.
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The first item of the optimization problem (3a) represents both the transmit power for a NRS in two TTIs and the transmit power for a relay for its proper data for only one TTI (expressed by the \(\frac {1}{2}\) factor). The second item of the optimization problem represents the transmit power consumed to transmit relayed data.
2.3 Relay selection strategy
2.3.1 Fixed relay selection
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Users with distance \(d_{k} < \frac {R}{3}\) will not have any advantage of being relayed because of their low distance to BS. Furthermore, they are far from cell border users so they are not seen as potential relays. Users with \(d_{k} < \frac {R}{3}\) will be thus non relayed sources and will not act as potential relays.
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Users with distance \(d_{k} > \frac {2R}{3}\) are in the cell border and will take advantage of being relayed if a user at mid distance from them and the BS exists. Users with \(d_{k} > \frac {2R}{3}\) are thus potential relayed sources.
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Users with distance \(\frac {R}{3} < d_{k} < \frac {2R}{3}\) can act as potential relays for users with \(d_{k} > \frac {2R}{3}\). Because of their relative low distance from the BS, these users will not be relayed.
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A mobile user with \(d_{k} > \frac {2R}{3}\) can have only one associated relay in order to lower signaling.
2.3.2 Joint relay selection, RB, and power allocation
3 Problem resolution
3.1 Optimal power allocation for a given resource block allocation and relay selection
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k is a not relayed source or a relay transmitting its own data in RB j:$$ \mathit{P_{k}^{(j)} = \left[\frac{\lambda_{k}}{\ln(2)}- \frac{1}{\gamma_{k,k}^{(j)}} \right]^{+}} $$(17)with [x]+= max {0,x}.
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k is a relayed source with relay rLet us first remind the throughput expression (1b):In cooperative mode, the total transmit power is minimized when the source and the relay forward the same amount of data. Consequently, the rate is the minimum of the rates on the two links (see Eq. (1b)). To achieve this, we assume that:$$ \mathit{R_{k}^{(j)}= \frac{1}{2} {\min} \left\{\log_{2}\left(1 + P_{k}^{(j)} \gamma_{k,r}^{(j)}\right); \log_{2}\left(1 + P_{r}^{(j)} \gamma_{r,r}^{(j)}\right)\right\}} $$$$ \mathit{P_{k}^{(j)} \ \gamma_{k,r}^{(j)} = P_{r}^{(j)} \ \gamma_{r,r}^{(j)}} $$(18)
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Solving problem (15) leads to the following expression for the power of the RS k in RB j:$$ \mathit{P_{k}^{(j)} = \left[ \frac{\lambda_{k} \ \gamma_{r,r}^{(j)}}{\ln(2)\left(\gamma_{k,r}^{(j)}+\gamma_{r,r}^{(j)}\right)} - \frac{1}{\gamma_{k,r}^{(j)}} \right]^{+}} $$(19)
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From Eq. (18), we obtain that the power of the relay r for the relayed data of RS k is: :$$ \mathit{P_{r}^{(j)} = \left[\frac{\lambda_{k} \ \gamma_{k,r}^{(j)}}{\ln(2)\left(\gamma_{k,r}^{(j)}+\gamma_{r,r}^{(j)}\right)} - \frac{1}{\gamma_{r,r}^{(j)}} \right]^{+}} $$(20)
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3.2 Optimal resource block allocation
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if k=r and k is a not relayed source:$$ \mathit{G_{k,r}^{(j)} = \lambda_{k} \ \log_{2}\left(1 + P_{k}^{(j)} \gamma_{k,k}^{(j)}\right) - P_{k}^{(j)}} $$(24)
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if k=r and k is a relay transmitting its own data in RB j:$$ \mathit{G_{k,r}^{(j)} = \frac {\lambda_{k}}{2} \ \log_{2} \left(1 + P_{k}^{(j)} \gamma_{k,k}^{(j)}\right) - \frac{1}{2} P_{k}^{(j)} } $$(25)
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if k is a relayed source and k≠r:$$ G_{k,r}^{(j)} =\frac{\lambda_{k}}{2} \log_{2}\left(1 + P_{k,r}^{(j)} \gamma_{k,r}^{(j)}\right) - \frac{1}{2} \left(P_{k,r}^{(j)} + P_{r,r}^{(j)}\right) $$(26)
3.3 Lagrangian variable update
3.4 Complexity and overhead comparison of the relay strategies
4 Performance evaluations
4.1 Performance results with fixed relay selection strategy
4.1.1 Optimality Evaluation
Proposed | Exhaustive | Proposed | Exhaustive |
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with relay | with relay | without relay | without relay |
7.16 | 6.24 | 9.39 | 9.34 |
4.1.2 Convergence analysis
4.1.3 Achieved performances
4.2 Performance results with joint relay selection, RB, and power allocation
4.2.1 Achieved performances
NRS | RS | R | |
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Average ratio (%) | 11.3 | 53.1 | 35.6 |
Average distance to the BS (m) | 689 | 782 | 517 |