In this section, we discuss related works on hierarchical underlying CR systems. For downlink transmission, MIMO beamforming is thought as an important technique to deal with the interference control problem. The works [6–10] investigated the beamforming design in downlink scheme of a secondary CR system. The work [6]
proposed a joint beamforming and power control algorithm to minimize the transmit power of secondary system under the condition that the QoS requirement must be satisfied. The work [7] proposed a suboptimal beamforming and scheduling algorithm to maximize the sum rate of secondary system. A joint zero-forcing beamforming and user scheduling algorithm is proposed [8] to mitigate the the inter-cell interference.
A joint beamforming and power control algorithm designed by convex optimization is developed in [9] for sum-rate maximization. The work [10] solved the problem of joint power allocation, beamforming and scheduling design to maximize the sum rate of the secondary CR system under the interference constraint. The optimal solution is obtained by solving a convex problem in this work.
Next, we categorize the related work about power control, beamforming and/or scheduling design for the sum rate maximization and interference power control in the uplink scheme. The work of [11] created a new incentive function that puts the capacity of secondary system on the nominator and interference power of secondary system on denominator. It focused on the user selection issue. The user is scheduled to maximize the incentive function. This method doesn’t consider any interference threshold, but the simulation result shows that it can keep the interference power to
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primary users under a certain level. The works of [12] and [13] are dedicated to the design of beamforming and power allocation. [12] used QR decomposition to simplify the MIMO channel matrix. According to the Q, R and Λ matrix, the beamforming weight is decided in a proper order by using successive interference cancellation (SIC) method. Then, they allocate the transmit power of each user by solving a sum-rate maximization problem with interference power constraints. The problem can be solved by using water filling principle. [13] formulated a optimization problem which aims to minimize the maximum interference to the primary users while guaranteeing the QoS of secondary network. The suboptimal solution of beamforming weights and transmit power is obtained jointly by genetic algorithm. Two interference-aware joint quantised power control and user scheduling algorithms are proposed in [14].
This work investigate an optimization problem to maximize the sum-rate capacity of the cognitive system under the constraint that the interference to the primary user is below a specified level. The main contribution of this work is the complexity analysis. They showed that the complexity of proposed suboptimal algorithms is much lower than exhaustive search but the performance of the three algorithms is close to each other. Finally, one thing needs to be noticed, all the works mentioned above use complex Gaussian variable to generate users’ channels in their simulators.
We compare our work with above research in Table 2.1.
Based on the above discussions, we can summarize that the optimal design of power allocation, beamforming, and scheduling in downlink transmission has been completed. The problem of beamforming and scheduling design in uplink transmis-sion is not investigated. Our work tries to guarantee the maximum sum rate of the secondary CR system while minimizing the interference to primary system. We use a more realistic spatial channel model (SCM) and 3GPP simulation parameters in our simulator which is different from other existing works.
Table 2.1: Literature Survey
Power Control Beamforming Scheduling
[11] Equal power x
1×1 transmission o
Maximize an incentive function
[12] Water filling QR decomposition
& SIC x
Sum rate maximization
[13]
Joint design by genetic algorithm x
Minimize the maximum ICI to primary system
[14]
Quantized
x Iteratively select a user
control causing minimum ICI
Sum rate maximization, but the sum rate ignores primary ICI Our works
Equal power Design by
Orthogonality convex optimization
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CHAPTER 3
System Model and Problem Formulation
We consider a hierarchical underlying CR system, consisting of a primary system and secondary system. The primary system owns a licensed spectrum. The secondary system aims to provide services to secondary users under the condition that it can not interfere with the primary system. In the fourth generation (4G) of cellular wireless standards, the frequency division duplex (FDD) and time division duplex (TDD) are both considered. Therefore, what kind of duplexing modes of the primary and secondary is most suitable for hierarchical underlying CR system should be discussed.
If the primary system is TDD, the secondary system may interfere primary downlink and uplink in one transmission time for both TDD and FDD secondary systems as shown in Fig. 3.1. The interference to primary system would hardly be managed.
If the primary system is FDD, the secondary systems can transmit at the primary downlink or uplink spectrum. The secondary system utilizing the uplink spectrum of primary users is a better option for two reasons. First, the quality of service (QoS) requirement of uplink is usually less strict than downlink. Thus, it may endure larger interference from secondary system. Secondly, in order to cancel the interference, the channel state information (CSI) of the entire system must be known at the secondary base station. If secondary system utilize the uplink spectrum of primary system, the channels from primary users can be estimated directly. If utilizing downlink spectrum, on the other hand, the CSI estimation would become indirect. Therefore, secondary
Primary
Figure 3.1: Spectrum usage of hierarchical CR system with FDD primary system and TDD/FDD secondary system.
system underlying the primary uplink spectrum is considered as shown in Fig. 3.2. To summarize, FDD primary system and TDD secondary system utilizing the primary uplink spectrum is considered in the thesis.
In order to avoid interference to primary systems, spectrum sensing is an im-portant functionality required in a CR system. Cognitive radio frame structure has been defined by IEEE 802.22. Each radio frame consisting of sensing period and data transmission period is shown in Fig. 3.3. In the sensing period, the CR system should stop transmission and receive the signal from primary system. Thus, the cognitive receiver can detect the existence of primary transmitters and estimate channel of the
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Secondary DL
Figure 3.2: Spectrum usage of hierarchical CR system with TDD primary system and FDD/TDD secondary system.
transmitters. We assume the channels between primary users and the secondary base station can be estimated in the sensing period if the two systems are synchronized.
Besides, the secondary base station can overhear the control channel of the primary system. So, the secondary base station knows the channels of PU-SBS and SU-SBS links perfectly. In addition to the above description, we assume that the secondary base station also knows the CSI of SU-PBS links which is much difficult to be realized.
It can be achieved if the primary base station has the spectrum sensing ability and
Figure 3.3: Cognitive radio frame structure in IEEE 802.22.
cooperates with the secondary base station. The other way is that secondary base station uses statistic channel model of the area to estimate the SU-PBS channels by knowing the locations of secondary users and primary base station.
The uplink channel model of hierarchical underlying CR system with primary system and secondary system is shown in Fig. 3.4. Primary users and the secondary users are equipped with single antenna. Each of the secondary and primary base station is equipped with M antennas. The secondary BS serve M secondary users at the most, which is selected from K secondary users, where K > M . The secondary base station has global CSI information of the entire CR system.
3.1 Signal Model for Multi-Carrier Hierarchical Cognitive Radio System
Since a OFDM symbol encodes data on multiple orthogonal narrow band subcarriers, we can process the signal in the frequency domain and obtain desirous data on each subcarrier of which the channel is flat fading. Let sk,nsc and ˜sk,nsc denote the trans-mitted signals from k-th secondary user to the secondary BS and k-th primary user to the primary BS, respectively. An M× 1 vector wk,nsc represents beamforming weight for the k-th secondary user. S is the set of served users, where S ⊆ {1, · · · , K}.
Then, the received signal of the k-th secondary user on the nsc-th subcarrier can be
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Figure 3.4: Hierarchical cognitive radio networks with a primary system and a sec-ondary system, where the uplink spectrum of the primary system is shared by the secondary system.
where hk,nsc denotes channel between M antennas of secondary BS and the k-th secondary user, √
Qp and √
Qs denote the transmit power of the primary user and the secondary user on a subcarrier respectively, gk,nsc denotes MIMO channel vector between secondary BS and k-th primary user, Sp is the set of scheduled primary users, and N is a Gaussian noise for secondary BS with zero mean and variance σN2. In addition, assuming the beamforming weight for k-th primary user is ˜wk,nsc, the
received signal at the primary BS can be written as following by exchange sk,nsc and
where ˜hk,nsc and ˜gk,nsc denote the MIMO channel vector of k-th primary user and secondary user to the primary BS respectively. ˜N is the Gaussian noise for primary BS.
We assume that the average power of signal E[
|sk,nsc|2]
and E[
|˜sk,nsc|2] is normalized to one. Thus, according to (3.1) the received signal SINR for the k-th secondary user in the nsc subcarrier is given by
γk,nsc =
Similarly, the SINR of primary user k is derived by (3.2) as:
˜
If there is no ISI, then we can design beamforming weights at each subcarrier to cancel the interference on the denominator.
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3.2 Performance Metrics
3.2.1 System Sum Rate
We consider a multi-user MIMO system, and utilize Shannon capacity formula to model the system sum rate as follows:
Csum =∑
k∈S
log2(1 + γk) , (3.5)
where S is the set of served users in each transmission; γk is the signal to interfer-ence and noise ratio (SINR) of the k-th user. The sum rate of secondary system is considered as the main performance metric in our work.
3.2.2 Interference Power and Channel Correlation
For a hierarchical CR system, the interference to the primary system should be limited strictly. According to (3.4) the inter-cell interference power for the primary BS to receive i-th PU’s signal on subcarrier nsc:
PICI(i, nsc) = Qs∑
j∈S
˜w†i,nscg˜j,nsc 2 (3.6)
Therefore, we can set appropriate transmit power for scheduled secondary users to limit the inter-cell interference (ICI) shown in (3.6) to any predefined threshold through simulation. Moreover, we design a scheduling algorithm to lower the in-terference while choosing the users who have better CSI for the secondary BS. It is very common to schedule users by the orthogonality of channel vectors in multi-user MIMO system. It is more likely to distinguish data through receive beamforming when the channel vectors of different users are more unalike. A metric called channel correlation is defined in [8] to evaluate the orthogonality between two channel vectors h and g:
Ω(h, g) = h†g
||h|| ||g|| (3.7)
We will use this metric to estimate the influence of a certain secondary user on the served primary users and decide which secondary user can be selected.