1 Introduction
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A heuristic approach is proposed for a multiuser underlay cognitive radio system. This heuristic is designed for the perfect CSI scenario by considering a cooperative underlay cognitive system. A complete resource allocation problem is addressed in three steps:
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The decoding strategies are identified per subcarrier for each user according to several conditions that will be defined later.
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A subcarrier allocation algorithm is described to choose the active subcarriers per user. Only one SU is activated per subcarrier following a criterion derived from the single-user algorithm.
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An optimization problem is then formulated, independently for each user, in order to maximize the secondary rate and the sum rate of the system under the constraint of power budget of each user and the maximum allowable interference on the PU.
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Motivated by the alternating optimization method [33], we propose an approach that sequentially solves a feasibility problem using dual decomposition.
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We identify several decoding strategy areas for different scenarios based on the mobile positions when two users exist in the secondary cell.
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We investigate the same problem for two secondary users under the assumption that imperfect CSI on the links between both primary and secondary transmitters and the primary receiver is available at the secondary user. This study can be easily extended to more than two secondary users.
2 System model and problem formulation
2.1 System model
2.2 Problem formulation
3 Resource allocation with perfect CSI
3.1 Description of the algorithm
3.2 Decoding strategies and achievable rates at the secondary receiver
3.3 Subcarrier allocation
3.4 Power allocation optimization
Conditions | Decoding strategies |
\(P_{s_{u_{[k]}},n}^{k}\)
|
---|---|---|
\(P_{p,(n-1)}^{k}= 0\) any value for a
k
and c
k
| Interweave |
\(\left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}\)
|
\(P_{p,(n-1)}^{k}\neq 0\) {a
k
=0;c
k
=0} | Int = noise |
\(\text {min}\left \{\left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \}\)
|
\(P_{p,(n-1)}^{k}\neq 0 \left \{a^{k} <0; c^{k} > 0\right \}\)
| SIC | 0 |
SC |
\(\text {min}\left \{\text {max}\left \{\left [\frac {1}{\hat {\mu _{s,n}}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {n_{0}\left (|h^{k}_{pp}|^{2} - |h^{k}_{sp}|^{2}\right)}{|h^{k}_{sp}|^{2} |h^{k}_{ps_{u_{[k]}}}|^{2}}\right \}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \} \)
| |
\( P_{p,(n-1)}^{k}\neq 0 \left \{a^{k} >0; c^{k} < 0\right \}\)
| SIC |
\(\text {min}\left \{\left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \}\)
|
SC | 0 | |
\(P_{p,(n-1)}^{k}\neq 0 \left \{a^{k} <0; c^{k}<0\right \}\)
| SIC |
\(\text {min}\left \{\frac {c^{k}}{a^{k}}; \left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \}\)
|
SC |
\(\text {min}\left \{\text {max}\left \{\left [\frac {1}{\hat {\mu _{s,n}}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {n_{0}\left (|h^{k}_{pp}|^{2} - |h^{k}_{sp}|^{2}\right)}{|h^{k}_{sp}|^{2} |h^{k}_{ps_{u_{[k]}}}|^{2}}; \frac {c^{k}}{a^{k}}\right \}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \} \)
| |
\(P_{p,(n-1)}^{k}\neq 0 \left \{a^{k} >0; c^{k}>0\right \}\)
| SIC \(\text {if} \frac {c^{k}}{a^{k}}\leq \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}} \)
|
\(\text {min}\left \{\text {max}\left \{\left [\frac {1}{\mu _{s,n}} - \frac {1}{b_{s,(n-1)}^{k}}\right ]^{+}; \frac {c^{k}}{a^{k}}\right \}; \frac {I_{\text {th}}^{k}}{\left |h_{ps_{u_{[k]}}}^{k}\right |^{2}}\right \} \)
|
otherwise | 0 | |
SC |
\(\min \left \{\max \left \{\left [\frac {1}{\mu ^{\wedge }_{s,n}}-\frac {1}{b^{k}_{s,(n-1)}}\right ]^{+} ;\frac {n_{0}\left (\left |h^{k}_{pp}\right |^{2}-\left |h^{k}_{sp}\right |^{2}\right)}{\left |h^{k}_{sp}\right |^{2}\left |h^{k}_{ps_{u_{[k]}}}\right |^{2}}\right \}; \frac {c^{k}}{a^{k}};\frac {I^{k}_{\text {th}}}{\left |h^{k}_{ps_{u_{[k]}}}\right |^{2}}\right \}\)
|
Cases |
\(b_{s,(n-1)}^{k}\)
|
\(P_{p,(n-1)}^{k}\neq 0\) and \(\left |h_{sp}^{k}\right |^{2} \leq \left |h_{ss_{u_{[k]}}}^{k}\right |^{2}\)
|
\(\frac {\left |h_{ss_{u_{[k]}}}^{k}\right |^{2}}{n_{0}+ \left |h_{sp}^{k}\right |^{2} P_{p,(n-1)}^{k}} \)
|
\(P_{p,(n-1)}^{k}\neq 0\) and \(\left |h_{sp}^{k}\right |^{2} > \left |h_{ss_{u_{[k]}}}^{k}\right |^{2}\)
|
\(\frac {\left |h_{ss_{u_{[k]}}}^{k}\right |^{2} }{n_{0}}\)
|
\(P_{p,(n-1)}^{k}=0\)
|
\(\frac {\left |h_{ss_{u_{[k]}}}^{k}\right |^{2} }{n_{0}}\)
|
Cases |
a
k
|
\(P_{p,(n-1)}^{k}\neq 0\) and \(\left |h_{sp}^{k}\right |^{2}\geq \left |h_{ss_{u_{[k]}}}^{k}\right |^{2}\)
|
\(\left |h_{sp}^{k}\right |^{2} \left |h_{ps_{u_{[k]}}}^{k}\right |^{2} - \left |h_{pp}^{k}\right |^{2} \left |h_{ss_{u_{[k]}}}^{k}\right |^{2}\)
|
All other cases | 0 |
Cases |
c
k
|
\(P_{p,(n-1)}^{k}\neq 0\) and \(\left |h_{sp}^{k}\right |^{2}\geq \left |h_{ss_{u_{[k]}}}^{k}\right |^{2}\)
|
\(n_{0} \left (\left |h_{pp}^{k}\right |^{2} - \left |h_{sp}^{k}\right |^{2} \right)\)
|
All other cases | 0 |
4 Algorithm evaluation with imperfect CSI
4.1 System parameters
4.2 Algorithm
5 Simulation results
5.1 Simulation results with perfect CSI
5.1.1 Performance evaluation for one secondary user
5.1.2 Statistics
5.1.3 Rates improvement and comparison with several methods
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The case where the secondary system is always switched off (denoted by “RP” for “Reference on Primary”). In this case, waterfilling is applied on the primary user and the complexity is calculated as O(L log2L) [35].
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The classical power allocation scheme where the secondary system can transmit on the whole bandwidth of a cognitive underlay/interweave system by considering the primary system’s interference as noise in all subcarriers. This algorithm is denoted by “FB” for “Full Band” and its complexity is 2·N·O(L log2L), with N as the number of iterations.
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An algorithm where the secondary system can only transmit in the subcarriers with weak interference (\(|{h^{k}_{sp}} |^{2} \leq | {h^{k}_{ss}} |^{2}\)) by considering the primary system’s interference as noise in these subcarriers. This algorithm is denoted by “PB” for “Partial Band,” and its complexity is 3/2·N·O(L log2L).
5.1.4 Performance evaluation with several secondary users
5.2 Simulation results with imperfect CSI
6 Conclusions
7 Appendix 1
7.1 Proof of Eq. (8)
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Step 1: \(x_{s}^{k,(1)}\) is decoded from \(y^{k}_{s}\) by treating \(\sqrt {\alpha ^{k}} h^{k}_{ss}x_{s}^{k,(2)} + h^{k}_{sp}x^{k}_{p}\) as noise, then \(y^{k^{\prime }} = y^{k} - h^{k}_{ss} \sqrt {(1 - \alpha ^{k})}x_{s}^{k,(1)}\) is obtained. The achievable rate is equal to:$$ R_{s}^{k,(1)} =\frac{B}{L} \log_{2}\left(1+ \frac{\left(1-\alpha^{k}\right)|h^{k}_{ss}|^{2} P^{k}_{s}}{\alpha^{k}|h^{k}_{ss}|^{2} P^{k}_{s} + |h^{k}_{sp}|^{2} P^{k}_{p} + n_{0}}\right) $$
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Step 2: \(x^{k}_{p}\) is decoded from \(\phantom {\dot {i}\!}y^{k^{\prime }}\) by treating \(\sqrt {\alpha ^{k}} h^{k}_{ss}x_{s}^{k,(2)}\) as noise, then \(\phantom {\dot {i}\!}y^{k^{\prime \prime }} = y^{k^{\prime }} - h^{k}_{sp}x^{k}_{p}\) is obtained. Thus, we have$$ R^{k}_{p} = \frac{B}{L} \log_{2}\left(1+ \frac{|h^{k}_{sp}|^{2} P^{k}_{p}}{\alpha^{k} |h^{k}_{ss}|^{2} P^{k}_{s} + n_{0}}\right) $$
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Step 3: \(x_{s}^{k,(2)}\) is decoded from \(\phantom {\dot {i}\!}y^{k^{\prime \prime }}\). Consequently$$R_{s}^{k,(2)} = \frac{B}{L} \log_{2}\left(1+ \frac{\alpha^{k} |h^{k}_{ss}|^{2} P^{k}_{s}}{n_{0}}\right) $$