Dynamic Spectrum Management pp 87120  Cite as
Concurrent Spectrum Access
Abstract
Concurrent spectrum access (CSA), which allows different communication systems simultaneously transmit on the same frequency band, has been recognized as one of the most important techniques to realize the dynamic spectrum management (DSM). By regulating the interference to be received by primary users, the secondary users are able to gain continuous transmission opportunity. Without the need of frequent spectrum detection and reconfiguration, the CSA has the merit of low cost and easy implementation in practice. In this chapter, we will present some important CSA models, discuss the key problems existing in these CSA systems, and review the techniques to deal with these problems.
4.1 Introduction
Compared with the opportunistic spectrum access (OSA), in recent years, the concurrent spectrum access (CSA) has been attracting increasing interests from academia and industry [1, 2]. The main reason is threefold. Firstly, the CSA allows one or multiple secondary users (SUs) simultaneously transmit on the primary spectrum, provided that the interference to the primary users (PUs) can be regulated. Thus, the SUs can transmission continuously regardless whether the PU is transmitting or not. Secondly, neither inquiry of geolocation database nor spectrum sensing is needed, and thus frequent spectrum reconfiguration can be avoided. This makes the cognitive device be with lowcost hardware, which is thus more easier to be deployed. Thirdly, the CSA can achieve higher area spectral efficiency due to its spatial reuse of spectrum [3, 4], and therefore, can be used to accommodate the dense wireless traffic in hostspot areas.
To enable CSA, the secondary transmitter (SUTx) needs to refrain the interference power produced to primary receiver (PURx) by designing its transmit strategy, such as transmit power, bitrate, bandwidth and antenna beam, according to the channel state information (CSI) of the primary and the secondary systems. Mathematically, the design problem can be formulated to optimize the secondary performance under the restrictions of the physical resource limitation of secondary system and the protection requirement of primary system. The physical resource constraint has been taken into consideration in the transmission design for the traditional communication system with dedicated operation spectrum [5, 6, 7]. While, the additional primary protection constraint poses new challenges to the design of both singleantenna and multiantenna CSA systems.
According to whether the interference temperature is explicitly given, the primary protection constraint is rendered in two forms. When the interference temperature is given as a predefined value, the primary protection constraint can be explicitly expressed as interference power constraint. There are basically two types of interference power constraint which are known as peak interference power constraint and average interference power constraint [8]. Peak interference power constraint restricts the interference power levels for all the channel states, while the average interference power constraint regulates the average interference power across all the channel states. The peak interference power constraint is more stringent with which the PUs can be protected all the time. Thus, it is suitable for protecting the PUs with delaysensitive services. The average interference power constraint is less stringent compared with the former one, since it allows the interference power exceed the interference temperature for some channel states. Thus, it is suitable to protect the PUs with delayinsensitive services. On the other hand, when the explicit interference temperature is unavailable, primary performance loss constraint is used to protect the PUs [9, 10]. In fact, this is a fundamental formulation of primary protection constraint, and can help the SUs to exploit the sharing opportunity more efficiently. However, this constraint requires the information including the CSI of the primary signal link and the transmit power of the PU, which is hard to be obtained in practice due to the lack of cooperation between the primary and secondary systems.
The research on the CSA system with SUs being equipped with single antenna mainly focuses on the analysis of secondary channel capacity. It has been shown that the capacity of secondary system with fading channel exceeds that with additive white Gaussian noise (AWGN) channel, under the interference power constraint [11]. The reason lies in that the fading channel with variation can provide more transmission opportunities for the secondary system. For flatfading channel, the secondary channel capacity under the peak and the average interference power constraints are studied in [12], whereas the ergodic capacity and the outage capacity under various combinations of the peak/average interference power constraint and the peak/average transmit power constraint are studied in [13]. It shows that the capacity under the average power constraint outperforms that under the peak power constraint, since the former one can provide more flexibilities for the SU transmit power design. In [9], the ergodic capacity and the outage capacity under the PURx outage constraint are analysed. It shows that to fulfill the same level of outage loss of PURx, the SU can achieve larger transmission rate under the PU outage constraint. With zero outage loss permitted, the SU still achieves scalable transmit rate with the PU outage constraint. In [14], the primary channel information is exploited to further improve the secondary performance. To predict the interference power received by the PURx, the CSI from the SUTx to the PURx, which is referred to as cross channel state information (CCSI), should be known by the SUTx. The mean secondary link capacity with imperfect knowledge of CCSI is addressed in [15]. To protect the PU under imperfect CCSI, it is shown that the interference temperature should be decreased, which thus leads to a decrement of secondary link capacity.
The use of multiple antennas provides both multiplexing and diversity gains in wireless transmissions [16, 17]. In particular, its function of cochannel interference suppression for multiuser transmission makes it a promising technique to enhance the CSA performance [18]. Generally speaking, multiple antennas can provide the SUTx in an CSA system more degrees of freedom in space, which can be split between the signal transmission to maximize the secondary transmit rate and the interference avoidance for the PUs. In [19], the multipleinput multipleoutput (MIMO) channel capacity of the SU in a multiantenna CSA system has been investigated. It shows that the primary protection constraint makes the methods proposed for the traditional MIMO system inapplicable for the CR transmit and receive design. Similar to the singleantenna CSA, moreover, the CCSI is critical for the transmit design for interference avoidance in the multiantenna CSA. In [20], it shows that when the effective interference channel can be perfectly estimated, the interference power received by the PUs can be perfectly avoided via cognitive beamforming. In [21], it further shows that the joint transmit and receive beamforming can effectively improve the secondary transmit rate by suppressing the interference produced by the PUTx. The use of multiple antennas also facilitates the multiple access and the broadcasting of secondary system [22]. Similar to the singleantenna case, due to the restriction of both transmit power and interference power, the transmit and receive design for the traditional multipleaccess channel and the broadcasting channel in multiantenna system is inapplicable and thus should be revisited [23, 24]. Moreover, the design for multiantenna CSA should take into consideration the uncertainty in the estimated channel [25, 26] and the security issue [27, 28].
In the remainder of this chapter, we first present the singleantenna CSA system and discuss the optimal transmit power design under different types of power constraint to maximize the secondary channel capacity. Then, the multiantenna CSA is discussed and the transceiver beamforming is presented under the condition of known and unknown related CSI. After that, the transmit and receive design for the cognitive multipleaccess channel and the cognitive broadcasting channel are presented, which is followed by the discussion of robust design for the multiantenna CSA. As an application of CSA in practice, the spectrum refarming technique is presented. Finally, the chapter is concluded with a summary.
4.2 SingleAntenna CSA
4.2.1 Power Constraints
In this CR system, the SUTx needs to regulate its transmit power to protect the PU service. There are mainly two categories of power constraints, which are the transmit power constraint and the primary protection constraint.
(1) Transmit Power Constraint
(2) Primary Protection Constraint
 Interference power constraint: When the peak or average interference temperature, which are respectively denoted by \(Q_{pk}\) and \(Q_{av}\), can be known by the SUTx, the primary protection constraint can be expressed as the interference power constraint, i.e.,$$\begin{aligned} g_\mathrm{sp} P(\nu ) \le&\, Q_{pk}, ~\forall \nu \end{aligned}$$(4.4)Equation (4.4) is known as the peak interference power constraint. It can be seen that the PU under this constraint can be fully protected at any fading status; thus, this constraint is suitable for protecting the delaysensitive services. Equation (4.5) is known as the average interference power constraint. Since this constraint only protects the PU in a longterm sense, and there can be cases that the interference power exceeds the interference temperature at some fading states. Thus, it is suitable to protect the delayinsensitive services.$$\begin{aligned} \mathbb E[g_\mathrm{sp} P(\nu )] \le&\, Q_{av} \end{aligned}$$(4.5)
 Primary performance loss constraint: When the peak or average interference temperature is not available, the primary protection constraint can be formulated as$$\begin{aligned} \varepsilon _p&\le \varepsilon _0, \end{aligned}$$(4.6)Equation (4.6) is known as the PU outage constraint [29], in which \(\varepsilon _0\) denotes the target outage probability of the PU that should be maintained, and \(\varepsilon _p\) is the outage probability of PU under the cotransmission of SU. Letting \(\gamma _p\) be the target signaltointerferenceplusnoise ratio (SINR) of the PU, \(\varepsilon _p\) can be derived as \( \varepsilon _p = \mathrm{Pr}\left\{ \frac{g_\mathrm{pp} P_p}{g_\mathrm{sp} P(\nu ) + N_0} < \gamma _p \right\} \). Equation (4.7) is known as the primary rate loss constraint [10], in which \(\delta _0\) is the maximum rate loss that is tolerable by the PU.$$\begin{aligned} \Delta r_p&\le \delta _0, ~\forall \nu \end{aligned}$$(4.7)
Note that in either (4.6) or (4.7), the primary system information, including \(g_\mathrm{pp}\) and \(P_p\) should be known by the SUTx. Such information can be transmitted from PU to SU if the cooperation between the two systems is available. When the intersystem cooperation is unavailable, the authors in [14] propose a scheme to allow the SUTx send probing signal which triggers the power adaptation of primary system. By doing so, the information of primary system can be exploited to improve the performance of secondary system.
4.2.2 Optimal Transmit Power Design
The transmit power of the SU can be optimized to achieve different kinds of secondary channel capacity. Here, we discuss the optimization of the SU transmit power for maximizing the ergodic capacity and minimizing the outage capacity of secondary system under different power constraints, respectively.
(1) Maximizing Ergodic Capacity

P41 and P42 have structural optimal solutions. For example, in P41, under the peak transmit and peak interference power constraints (\(\mathcal F_1\)), \(P(\nu )=P_{pk}\) when \(g_\mathrm{sp}<\frac{Q_{pk}}{P_{pk}}\). When \(g_\mathrm{sp}\ge \frac{Q_{pk}}{P_{pk}}\), the optimal transmit power follows channel inversion with \(g_\mathrm{sp}\), i.e., \(P(\nu )=\frac{Q_{pk}}{g_\mathrm{sp}}\). This indicates that deep fading in the interference channel is helpful to the secondary performance. Under the average transmit and peak interference power constraints (\(\mathcal F_3\)), the SU transmit power is capped by \(\frac{Q_{pk}}{g_\mathrm{sp}}\), and is decided by \(g_\mathrm{sp}\) and \(g_\mathrm{ss}\) simultaneously. Specifically, the transmit power is higher when the interference channel suffers from deep fading while the secondary signal channel is not faded. In P42, under the peak transmit and peak interference power constraints (\(\mathcal F_1\)), \(P(\nu )\) has the truncated channel inversion structure which is similar to the conventional fading channel [5]. The difference lies in that the condition for channel inversion here is determined by both the secondary signal channel and the interference channel, while that in [5] it is determined by signal channel solely. Therefore, this power allocation strategy is also referred to as twodimensionaltruncated channelinversion (2DTCI).

For both problems, the average interference power constraint is superior to the peak counterpart, as the former one provides more flexibility to the power allocation of the SU. Specifically, with the average interference power constraint, more power can be used when the interference channel experiences deep fading while the secondary signal channel is not faded.

For both problems, the primary performance loss constraint is superior to the peak interference power constraint, since the SU can transmit more opportunistically with the former constraint. Moreover, when no additional outage of the PU is allowed, the SU transmission is not possible under the peak interference power constraint. However, under the primary performance loss constraint, the SU transmission is not only allowed, but also sustains capacity increase with the transmit power.
4.3 Cognitive Beamforming
A model of CB is shown in Fig. 4.2, where an SUTx transmits signal to the SURx by concurrently sharing the spectrum of primary system in which two PUs communicate with each other. The SUTx is required to be equipped with more than one antennas, and the other terminals can be equipped with one or multiple antennas. Let \(M_{1}\), \(M_{2}\), \(M_\mathrm{st}\), and \(M_\mathrm{sr}\) be the number of antennas on PU\(_1\), PU\(_2\), SUTx and SURx, respectively. The fullrank transmit beamforming matrix of PU\(_j\) is denoted by \(\mathbf A_j \in {\mathbb C}^{M_j\times d_j}\) where \(j\in \{1,2\}\), \(d_j\) denotes the corresponding number of transmit data streams and \(1\le d_j \le M_j\). Then, the transmit covariance matrix of PU\(_j\) can be written as \(\mathbf S_j =\mathbf A_j \mathbf A_j^H \). The receive beamforming matrix of PU\(_j\) is denoted by \(\mathbf B_j\in \mathbb C^{d_j\times M_j}\), where \(j\in \{1,2\}\). The primary terminals are considered to be oblivious to the SUs, and treat the interference from the SUTx as additional noise. In the secondary system, the transmit beamforming matrix of the SUTx is denoted by the fullrank matrix \(\mathbf A_c\in \mathbb C^{M_\mathrm{st}\times d_c}\), where \(d_c\le M_\mathrm{st}\). Then, \(\mathbf S_c=\mathbf A_c\mathbf A_c^H\) is the transmit covariance matrix of the SUTx. Finally, \(\mathbf H \in {\mathbb C}^{M_\mathrm{sr}\times M_\mathrm{st}}\) denotes the secondary signal channel matrix and \(\mathbf G_j \in {\mathbb C}^{M_\mathrm{sr}\times M_\mathrm{st}}\) denotes the matrix of interference channel from the SUTx to PU\(_j\).
4.3.1 Interference Channel Learning
To get some knowledge of the interference channel, a viable way is to allow the SUTx listen to the signal sent by the PUs before its own transmission, and estimate the channel from the PUs to the SUTx. Since the system operates at timedivision duplex (TDD) mode, the estimated channel can be treated as the interference channel from the SUTx to the PUs according to channel reciprocity. This process is referred to as channel learning. The learningandtransmission protocol is illustrated in Fig. 4.3, in which T is the frame length, \(\tau \) is the time duration used for learning the interference channel and the remainder \(T\tau \) is used for data transmission.
4.3.2 CB with Perfect Channel Learning
In this part, the transmit beamforming at the SUTx, including the transmit precoding and power allocation, under perfect learning of EIC is discussed. In the EIC learning, the noise effect on estimating \(\mathbf Q_s\) based on \(\hat{\mathbf Q}_y\) can be completely removed by choosing a large enough N, i.e., \(N\rightarrow \infty \).
When the conditions \(\mathbf A_j^H \mathbf G_j \sqsubseteq \mathbf B_j \mathbf G_j, j\in \{1,2\}\) hold,^{1} and one or both of the PUs have multiple antennas but transmit only through a subspace of the overall spatial dimensions, i.e., \(d_j<\min \{M_1, M_2\}\), the proposed CB scheme based on (4.15) outperforms the “PSVD” scheme proposed in [30] where \(\mathbf G_{j}\)’s are perfectly known by the SUTx, in terms of the achievable degree of freedom (DoF) of CR transmission. The reason lies in that the \(\mathbf G_\mathrm{eff}\) contains the information of \(\mathbf A_j^H \mathbf G_j\). Based on the condition \(\mathbf A_j^H \mathbf G_j \sqsubseteq \mathbf B_j \mathbf G_j\), \(\mathbf G_\mathrm{eff}\) also contains the information of \(\mathbf B_j \mathbf G_j\). Thus, the propose scheme can have a strictly positive DoF even when \(M_1+M_2\ge M_\mathrm{st}\), provided that \(d_1+d_2<M_\mathrm{st}\). In contrary, the \(\mathbf B_j \mathbf G_j\) is unknown in the PSVD scheme. Therefore, the DoF becomes zero when \(M_1+M_2\ge M_\mathrm{st}\). In most practical scenarios, it has \((d_1 + d_2) \le (M_1 + M_2)\), and thereby the DoF gain achieved by the proposed scheme (\((\min (M_\mathrm{st}d_1d_2)^+, M_\mathrm{sr})\)) is always no less than the DoF achieved by the PSVD (\((\min (M_\mathrm{st}M_1M_2)^+, M_\mathrm{sr})\)). Moreover, the maximum DoF is achieved when \(d_1=d_2=0\), i.e., the PU links are switched off.
4.3.3 CB with Imperfect Channel Learning: A LearningThroughput Tradeoff
In this part, the CB with imperfect estimation of EIC due to finite sample size is discussed. With finite N, the noise effect on estimating \(\mathbf Q_s\) cannot be removed, and thus error appears in the EIC estimation. Denote \(\hat{\mathbf G}_\mathrm{eff}\) as the estimated EIC with error. Recall the twophase protocol given in Fig. 4.3. It can be seen that the number of sample size N increases as the learning duration \(\tau \) increases. This improves the estimation accuracy of \(\hat{\mathbf G}_\mathrm{eff}\), and therefore contributes to the CR throughput. However, increasing the learning duration will lead to a decrement of data transmission duration, which harms the CR throughput. Given that the overall frame length is limited by the delay requirement of the secondary service, there exists an optimal learning duration that maximizes the CR throughput. This is the so called learningthroughput tradeoff in the CB design.
(1) Imperfect Estimation of EIC
 With known noise power: When the noise power \(\rho _0\) is known, the estimation of \(\mathbf Q_s\) based on the maximum likelihood criterion can be written aswhose rank is \(\hat{d}_\mathrm{eff}\). The first \(\hat{d}_\mathrm{eff}\) columns of \(\hat{\mathbf T}_y\) give the estimate of \(\mathbf V\), and the last \(M_\mathrm{st}\hat{d}_\mathrm{eff}\) columns of \(\hat{\mathbf T}_y\) give \(\hat{\mathbf U}\). This will be used to design the CB precoding matrix.$$\begin{aligned} \hat{\mathbf Q}_s = \hat{\mathbf T}_y \mathrm{Diag}\left( (\hat{\lambda }_1\rho _0)^+,\ldots , (\hat{\lambda }_{M_\mathrm{st}}\rho _0)^+ \right) \hat{\mathbf T}_y^H \end{aligned}$$(4.17)
 With unknown noise power: When the noise power \(\rho _0\) is unknown, the noise power should be estimated along with \(\hat{\mathbf Q}_s\). By obtaining \(\hat{\rho }_0, \hat{d}_\mathrm{eff}, \hat{\mathbf V}\) and \(\hat{\mathbf U}\), the maximum likelihood estimate of \(\mathbf Q_s\) can be derived aswhich has the same structure with (4.17).$$\begin{aligned} \hat{\mathbf Q}_s = \hat{\mathbf V} \mathrm{Diag}\left( \hat{\lambda }_1\hat{\rho }_0,\ldots , \hat{\lambda }_{\hat{d}_\mathrm{eff}}\hat{\rho }_0 \right) \hat{\mathbf V}^H \end{aligned}$$(4.18)
With \(\hat{\mathbf Q}_s\) being derived, the estimate of EIC can be determined according to (4.13).
(2) Interference Leakage to PUs

The upper bound is finite, since \(\alpha _j>0\);

The upper bound is invariant with any scaler multiplication with \(\mathbf G_j\). This means that the normalized interference received by each PU is independent with its position.

The upper bound is inversely proportional to the number of samples and the transmit power of the PU. Therefore, the PU with longer transmit time within the learning duration and/or with higher transmit power will suffer from less interference. This is the main principle based on which the SUTx designs a fair transmit scheme in terms of distributing the interference among PUs.
With the upper bound of interference leakage, the SINR of PU\(_j\), denoted by \(\gamma _j\), can be derived. Let \(\gamma =\min \limits _{j\in \{1,2\}}\{\gamma _j\}\). The threshold J in the constraint of P43 can be derived as \(J=\min \left( P_t, \gamma \tau \right) \) with peak transmit power constraint, and \(J=\min \left( \frac{T}{T\tau }P_t, \gamma \tau \right) \) with average transmit power constraint.
After \(\hat{\mathbf U}\) and J are determined, P43 can be solved. It can be seen that by introducing learning phase before data transmission, the multiantenna SUTx is able to estimate the interference channel information which is indispensable for interference control, and has a good balance between the interference avoidance and throughput maximization.
4.4 Cognitive MIMO

The spatial spectrum design for the SUTx under the condition that the secondary signal channel and the interference channel are perfectly known;

The joint transmit and receive beamforming for the SUs to avoid interference to the PUs and suppress interference from the PUs simultaneously, under the condition that the secondary signal channel and the interference channel are unknown.
The model of the cognitive multipleinput multipleoutput (MIMO) system is shown in Fig. 4.4, where a pair of SUs shares the same spectrum with K primary users. The number of antennas of PU k is denoted by \(M_k\), and the number of antennas of the SUTx and that of the SURx are denoted by \(M_\mathrm{st}\) and \(M_\mathrm{sr}\), respectively. The singleband frequency is shared by the primary and secondary systems. \(\mathbf H\in \mathbb C^{M_\mathrm{st}\times M_\mathrm{sr}}\) denotes the secondary signal channel matrix and \(\mathbf G_k \in \mathbb C^{M_k\times M_\mathrm{st}}\) denotes the interference channel matrix from the SUTx to PU\(_k\).
4.4.1 Spatial Spectrum Design
 Total interference power constraint: If the total interference power received by all the receive antennas of each PU is limited, the interference power constraint can be formulated aswhere \(Q_k\) is the total interference temperature of PU\(_k\).$$\begin{aligned} \mathrm{Tr}(\mathbf G_k\mathbf S\mathbf G_k^H) \le Q_k, ~ k=1,\ldots ,K \end{aligned}$$(4.23)
 Individual interference power constraint: If the individual interference power received by each antenna of the PU is limited, the interference power constraint can be formulated aswhere \(q_k\) is the individual interference temperature of PU\(_k\) on each of its antennas.$$\begin{aligned} \mathbf g_{k,j}\mathbf S\mathbf g_{k,j}^H \le q_k, ~ j=1,\ldots , M_k, ~k=1,\ldots ,K \end{aligned}$$(4.24)
4.4.1.1 One SingleAntenna PU
(1) MISO Secondary Channel, i.e., \(M_\mathrm{sr}=1\)
In this case, the rank of \(\mathbf S\) is larger than one, and thus spatial multiplexing is optimal instead of beamforming. In general, there is no closedform solution of the optimal \(\mathbf S\). Thus, two suboptimal algorithms that achieve the closedform solution of \(\mathbf S\) are proposed as follows.

DSVD:
Directchannel SVD (DSVD) method applies singular value decomposition (SVD) to the secondary signal channel matrix, which can be expressed as \(\mathbf H=\mathbf Q \mathbf \Lambda ^{1/2} \mathbf U^H\). Thus, the precoding matrix \(\mathbf V\) can be obtained as \(\mathbf V=\mathbf U\). Let \(M_s=\min \{M_\mathrm{st},M_\mathrm{sr}\}\). The optimal power allocation \(\mathbf p=[p_1,\ldots ,M_s]\) can be obtained by solvingwhere \(\lambda _i\) is the diagonal element of \(\mathbf \Lambda \), \(\alpha _i = \Vert \mathbf g\mathbf u_i\Vert ^2\) and \(\mathbf u_i\) is the ith column of \(\mathbf U\). The problem is shown convex and the closedform optimal \(p_i\) is given by$$\begin{aligned} \max \limits _{\mathbf p} ~~&\sum _{i=1}^{M_s}\log _2(1+p_i\lambda _i) \\ s.t. ~~&\sum _{i=1}^{M_s} p_i \le P_t \\&\sum _{i=1}^{M_s} \alpha _i p_i \le q \\&\mathbf p \succeq \mathbf 0 \end{aligned}$$(P47)where \(\nu \) and \(\mu \) are the nonnegative dual variables associated with the transmit power constraint and the interference power constraint, respectively. Therefore, it can be seen that by using DSVD method, the optimal power allocation for the MIMO secondary channel follows multilevel waterfilling form.$$\begin{aligned} p_i = \left( \frac{1}{\nu + \alpha _i\mu }  \frac{1}{\lambda _i}\right) ^+, ~i=1,\ldots , M_{s} \end{aligned}$$(4.25) 
PSVD:
Projectedchannel SVD (PSVD) method applies SVD to the projected channel of \(\mathbf H\), i.e., \(\mathbf H_\perp =\mathbf H(\mathbf I \hat{\mathbf g} \hat{\mathbf g}^H)\) with \(\hat{\mathbf g}=\mathbf g^H/\Vert \mathbf g\Vert \). Applying SVD to \(\mathbf H_\perp \) yields \(\mathbf H_\perp = \mathbf Q_\perp \mathbf \Lambda _\perp ^{1/2} (\mathbf U_\perp )^H\). Thus, the precoding matrix \(\mathbf V\) can be obtained as \(\mathbf V=\mathbf U_\perp \), and the optimal power allocation can be derived aswhere \(\lambda _i^\perp \) is the diagonal element of \(\mathbf \Lambda _\perp \) and \(\nu \) is the dual variable associated with the transmit power constraint. Here we can see that, by using PSVD, it has \((\mathbf U_\perp )^H \hat{\mathbf g}=0\). Since \(\mathbf S=\mathbf U_\perp \mathbf \Sigma (\mathbf U_\perp )^H\), we have \(\mathbf g \mathbf S\mathbf g^H=\mathbf 0\), which indicates that the interference power produced to the PU can be perfectly avoided.$$\begin{aligned} p_i = \left( \nu \frac{1}{\lambda _i^\perp }\right) ^+, ~i=1,\ldots , M_{s} \end{aligned}$$(4.26)
4.4.1.2 Multiple Multiantenna PUs
With multiple PUs which are equipped with single or multiple antennas, the transmission of the SUTx can be designed by considering the following two cases.
(1) MISO Secondary Channel, \(M_\mathrm{sr} = 1\)
(2) MIMO Secondary Channel, i.e., \(M_\mathrm{sr} > 1\)
4.4.2 LearningBased Joint Spatial Spectrum Design

The secondary signal channel and the interference channel are unknown;

The interference from the PUs is suppressed by designing the spatial spectrum at the SURx.
To enable the CR transmission, a threephase protocol is proposed as shown in Fig. 4.5, whose interpretation is as follows.

Channel Learning Stage: A duration of \(\tau _l\) is used for channel learning, in which the SUTx and SURx gain partial knowledge on the interference channel \(\mathbf G_1\) and \(\mathbf G_2\) via listening to the transmission of the PUs. Specifically, the SUs blindly estimate the noise subspace matrix from the covariance matrix of the received signal. It should be noted that, due to the finite number of samples, perturbation inevitably appears in the noise subspace matrix.

Channel Training Stage: Since the secondary signal channel is unknown by the SUTx, in the training stage with duration of \(\tau _t\), the SUs estimate the channel after applying joint transmit and receive beamforming. By considering the interference to and from the PUs, the optimal training structure can be derived to minimize the channel estimation error. It is noted that the channel to be estimated is not the actual channel from the SUTx to the SURx, but is the effective channel, which contains the information of transmit and receive beamforming matrices and the actual signal channel.

Data Transmission Stage: With the interference channel information learnt in the first stage and the signal channel information estimated in the second stage, the SUTx transmits signal during the data transmission stage with length of \(T\tau _l\tau _t\).
It is worth noting that the parameter \(\tau _l\) plays an important role in the CR performance. Intuitively, a larger \(\tau _l\) might be preferred in terms of better space estimation, so that the interference to and from the PUs can be minimized. However, increasing learning time will decease the data transmission time, if the training duration is fixed. This harms the CR throughput. Moreover, taking the interference constraints into consideration during training and data transmitting, the freedom of power allocation is reduced. Thus, to investigate the CR performance, the lower bound of the secondary ergodic capacity is evaluated, which is related to both the channelestimation error and the interference leakage to and from the PUs [33]. The lower bound of the CR ergodic capacity is then maximized by optimizing the transmit power and the time allocation over learning, training and transmission stages. A closedform optimal power allocation can be found for a given time allocation, whereas the optimal time allocation can be found via twodimensional search over a confined set [21].
4.5 Cognitive MultipleAccess and Broadcasting Channels
In the previous sections, the CR system under investigation has only one pair of SUs. In this section, we present the CR system that contains multiple transmitters or receivers, which forms the cognitive multipleaccess channel (CMAC) and the cognitive broadcasting channel (CBC), respectively.
4.5.1 Cognitive MultipleAccess Channel
(1) SumRate Maximization Problem
In P410, if the interference constraints are replaced with the single sum transmit power constraint, the optimal power allocation can be derived as the conventional waterfilling solution. The multiple interference power constraints complicate the solving of the problem, and thus, we solve the problem by considering the following two cases.

SinglePU case: When there is only one PU, and thus there remains one interference power constraint, the optimal power allocation follows waterfilling form. Different from the conventional waterfilling power allocation which has a common water level, this solution has different water levels for different SUs. Moreover, each water level is upperbounded by the individual maximum allowable transmit power. Therefore, this power allocation scheme is also referred to as capped multilevel (CML) waterfilling. Figure 4.7 gives an example of the CML waterfilling, where we can see that the power allocated to each SU is limited by the minimum value between its specific water level and the water cap.

MultiplePU case: The method to solve P410 with multiple interference constraints is summarized as follows. The method first removes the noneffective interference constraints. Suppose m effective constraints remain. It starts with the subproblems with a single interference constraint. For the case of i constraints, we select i out of N constraints (thus, there are \(\mathrm{C}_m^i\) combinations) and check whether the solution of the subproblems also satisfies the remained \((mi)\) constraints. If yes, this solution is globally optimal; otherwise, we continue to search the case of \((i+1)\).
4.5.2 Cognitive Broadcasting Channel

Total transmit power constraint: if \(\mathbf A\) is an identity matrix;

Individual transmit power constraint: if \(\mathbf A\) is a diagonal matrix in which one of the diagonal elements is one and the others are zeros;

Interference power constraint: if \(\mathbf A=\mathbf g\mathbf g^H\) where \(\mathbf g\) is the vector of channel response from the SU to the PU.
4.6 Robust Design
The CSI, including the CCSI and SCSI, is critical for the CR system to control interference and optimize its performance. In practice, the CSI obtained by the SU is normally imperfect, for which robust design is needed to be identified so that the cognitive transmission strategy is less sensitive to the uncertainty in the CSI. In the literature, there are a few of related robust designs. One kind of ideas is to design the robust beamforming so that a high probability that the interference power constraint is satisfied can be achieved. Another kind of ideas is to model the uncertainty in related CSI with boundary and design the robust beamforming to guarantee the interference power constraint. In this part, we consider two scenarios, i.e., only the CCSI contains uncertainty [38] and both of the CCSI and SCSI contain uncertainty [26], respectively.
4.6.1 Uncertain Interference Channel
4.6.2 Uncertain Interference and Secondary Signal Channels
4.7 Application: Spectrum Refarming
Applying the CSA technique in cellular networks is by no mean a trivial task [39]. Although the resource allocation for the traditional cellular networks has been extensively investigated both in singlecell [40] and multicell scenarios [41], the spectrum sharing among cellular networks is challenging due to the additional interference power constraint. Moreover, the concrete characteristics of each cellular network, such as the infrastructure deployment and the radio access technique (RAT) profoundly affect the CSA design. Quite a few of literatures have investigated the spectrum sharing between systems with the same RAT. For example, an orthogonal frequency division multiple access (OFDMA) secondary system shares the spectrum of an OFDMA primary system, or both of them are CDMAbased. In fact, due to the explosive growth of the fourth generation (4G) wireless traffic, spectrum sharing among OFDMA systems will be increasingly difficult as the 4G licensed spectrum has been crowded. In addition, since the 4G wireless network outperforms the second generation (2G) and the third generation (3G) in terms of peak data rate, latency and throughput, the legacy subscribers have been migrating to the 4G cellular networks. The outmoving of the legacy users decreases the utilization of the legacy licensed spectrum, which thus provides sharing opportunity for the 4G networks. To this end, the CSA between different generations of cellular networks, which is known as spectrum refarming (SR), attracts more attentions in recent years.
There are two SR models, i.e., the opportunistic SR model and the concurrent SR model, which are developed based on OSA and CSA, respectively.

Opportunistic SR allows the OFDMA system dynamically access the spectrum hole in the legacy bands. Due to the narrowband nature of global system for mobile communications (GSM), the SR on GSM spectrum belongs to this model. As the traffic of GSM decreases, there exist idle subbands that can be opportunistically accessed. The authors in [42] proposed an LongTerm Evolution (LTE)/GSM SR by reserving partial subbands for GSM transmission and controlling the transmit power for both GSM and LTE to refrain the intertechnology interference. This model was further extended to the heterogeneous cellular networks where the OFDMA small cells access the idle spectrum of the GSM macrocell [43].

Concurrent SR allows the different generations of networks cotransmit at the same legacy band, provided that the primary system can be protected. The SR between the OFDMA and CDMA systems belongs to this model, due to the wideband nature for both systems. Since the channel destroys the orthogonality among the CDMA users, there exists interuser interference which is related to the number of CDMA users [44]. When the number of CDMA users decreases, each CDMA user will experience less interuser interference. Thus, they can tolerate an amount of interference introduced by the OFDMA system, with which the target SINR of the CDMA user can be maintained.
In what follows, we discuss the OFDMA/CDMA concurrent SR. The key challenges to be addressed include: (1) Quantification of interference temperature: In related literatures, the interference temperature is usually given as a predefined threshold without any justification [45, 46]; (2) Joint optimization of the primary and secondary resource allocation: By taking the interference from the PUTx to the SURx into consideration, the primary and secondary power allocation can be jointly optimized through exploiting the primary inner power control scheme. (3) Robust power allocation: Without the information of CCSI, robust power allocation should be designed for the OFDMA system to provide sufficient protection to CDMA users. The study also extends to the SR of multiband CDMA system [47] and the heterogeneous SR systems [48, 49].
4.7.1 SR with Active Infrastructure Sharing
(1) Quantification of Interference Temperature
To quantify the interference temperature provided by the CDMA users, the SINR of CDMA users with the interference from OFDMA system should be derived. Given the number of CDMA users (denoted by U) and the spreading gain (denoted by N), the SINR of CDMA user is determined by the specific spreading codes assigned among users and the instantaneous SCSI of the CDMA system. Due to the lack of cooperation between the CDMA and OFDMA systems, these information is unknown by the OFDMA system, and thus it is hard for the OFDMA system to predict the CDMA SINR. By considering a largedimension system where \(U,N\rightarrow \infty \) and \(\frac{U}{N}\) approaches a finite constant, the SINR of the CDMA users approaches an asymptotic value which is independent with the specific codes and instantaneous SCSI. Thus, by limiting the asymptotic SINR to be no less than the target SINR, the closedform interference temperature can be obtained [51].
(2) Joint Resource Optimization of CDMA and OFDMA Systems
Note that the interference temperature of the CDMA system is a function of the transmit power of the CDMA user. A larger transmit power provides a higher interference temperature but also introduces higher interference to the OFDMA user. Thus, there exists an optimal CDMA transmit power to maximize the OFDMA throughput. An efficient algorithm was proposed in [52] to solve the joint resource optimization of the CDMA and OFDMA systems by investigating the convexity of the problem over the CDMA transmit power and the OFDMA resource allocation. Moreover, although the transmit power of CDMA and OFDMA systems are jointly optimized, it is unnecessary to inform the CDMA user with the optimal value of the transmit power in practice. In fact, once the OFDMA system operates with its optimal transmit power and subcarrier allocation, so as the CDMA system due to the inner power control of the CDMA system.
4.7.2 SR with Passive Infrastructure Sharing
Passive infrastructure sharing refers to the sharing of passive elements in their radio access networks, such as cell sites. When the SR technique is applied with passive infrastructure sharing, the licensed legacy system and the unlicensed system are equipped with separate BS antennas, as shown in Fig. 4.10 (Scenario II). Intuitively, this additional BS antenna should bring along more diversity that can be exploited by the OFDMA system to improve the refarming performance [11, 53, 54]. However, without active participation of the legacy system, it is difficult to obtain the CCSI, which is the necessary information for the OFDMA system to predict the produced interference.
To solve this problem, a robust resource allocation scheme was proposed in [55], where the SCSI of the OFDMA system is used as the CCSI to predict the interference power. It has been proved that under this scheme, the CDMA service can be overprotected, i.e., the actual interference power is always no larger than the interference temperature. Furthermore, to fully utilize the interference temperature, an iterative resource allocation scheme is proposed which gradually increases the transmit power of OFDMA users until the actual interference received by the CDMA system reaches the interference temperature.
4.7.3 SR in Heterogeneous Networks
To provide high throughput and seamless coverage for the wireless communications, small cells have been proposed to overlay the existing cellular networks [56]. Conventionally, small cells are deployed to share the radio spectrum by using the same RAT with the macrocell [57, 58]. By doing so, the small cells can offload macrocell traffic directly. However, they inevitably introduce interference to the macrocell users and thus degrade their performance. To address this problem, SR in heterogeneous networks is a viable solution.
Consider a heterogeneous network as shown in Fig. 4.10 (Scenario III), where multiple OFDMA small cells share the spectrum of CDMA macrocell. Specifically, the downlink of small cells share the spectrum used for the CDMA uplink, since the uplink traffic of the CDMA system is normally lighter than the downlink. By quantifying the interference power produced by each small cell, the resource allocation problem can be formulated, where the objective is to maximize the total throughput of all small cells and the constraints are the total interference power constraint and individual transmit power constraint. The problem is transformed to optimize the transmit power and the allocation of interference temperature among small cells [48].
In practice, due to the limited signaling between the macrocell and the small cells, the CCSI between the small cell BS (SBS) and macrocell base station (MBS) is usually absent. Since the CCSI accounts for the distancebased path loss, the smallscale fading and the largescale shadowing, only the latter two are to be determined, as the distance between SBS and MBS is fixed and can be easily known from the global geographical information. It is found that the optimal power allocation for the SR heterogeneous networks is essentially independent with the fading and shadowing components of the CCSI and is only related to the distancebased path loss. Therefore, the need of instantaneous information about the fading and shadowing of CCSI can be avoided.
4.8 Summary
In this chapter, we have discussed the CSA technique by introducing the singleantenna CSA system, the multiantenna cognitive beamforming, the cognitive MIMO, the CMAC and CBC, and the robust design for the CSA system. The application of the CSA technique to operating the LTE cellular system on the legacy spectrum, also known as the spectrum refarming, has been discussed. Several critical problems in the CSA have been addressed, including the absence of the interference channel and signal channel knowledge, the optimal beamforming and multiplexing, as well as the interference avoidance and suppression.
Footnotes
 1.
\(\mathbf X\sqsubseteq \mathbf Y\) means that for two given matrices with the same column size, \(\mathbf X\) and \(\mathbf Y\), if \(\mathbf X\mathbf e=0\) for any arbitrary vector \(\mathbf e\), then \(\mathbf Y\mathbf e=0\) always holds.
References
 1.L. Zhang, M. Xiao, G. Wu, M. Alam, Y.C. Liang, S. Li, A survey of advanced techniques for spectrum sharing in 5g networks. IEEE Wirel. Commun. 24(5), 44–51 (2017)CrossRefGoogle Scholar
 2.L. Zhang, Y.C. Liang, M. Xiao, Spectrum sharing for internet of things: a survey. IEEE Wirel. Commun. 26(3), 132–139 (2019)CrossRefGoogle Scholar
 3.Y. Kim, T. Kwon, D. Hong, Area spectral efficiency of shared spectrum hierarchical cell structure networks. IEEE Trans. Veh. Technol. 59(8), 4145–4151 (2010)CrossRefGoogle Scholar
 4.H.S. Dhillon, R.K. Ganti, F. Baccelli, J.G. Andrews, Modeling and analysis of ktier downlink heterogeneous cellular networks. IEEE J. Sel. Areas Commun. 30(3), 550–560 (2012)CrossRefGoogle Scholar
 5.A.J. Goldsmith, P.P. Varaiya, Capacity of fading channels with channel side information. IEEE Trans. Inf. Theory 43(6), 1986–1992 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
 6.E. Biglieri, J. Proakis, S. Shamai, Fading channels: informationtheoretic and communications aspects. IEEE Trans. Inf. Theory 44(6), 2619–2692 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
 7.Y.C. Liang, R. Zhang, J.M. Cioffi, Subchannel grouping and statistical waterfilling for vector blockfading channels. IEEE Trans. Commun. 54(6), 1131–1142 (2006)CrossRefGoogle Scholar
 8.R. Zhang, On peak versus average interference power constraints for protecting primary users in cognitive radio networks. IEEE Trans. Wirel. Commun. 8(4), 2112–2120 (2009)CrossRefGoogle Scholar
 9.X. Kang, R. Zhang, Y.C. Liang, H.K. Garg, Optimal power allocation strategies for fading cognitive radio channels with primary user outage constraint. IEEE J. Sel. Areas Commun. 29(2), 374–383 (2011)CrossRefGoogle Scholar
 10.R. Zhang, Optimal power control over fading cognitive radio channel by exploiting primary user CSI. IEEE Glob. Commun., pp. 1–5 (2008)Google Scholar
 11.A. Ghasemi, E.S. Sousa, Fundamental limits of spectrumsharing in fading environments. IEEE Trans. Wirel. Commun. 6(2), 649–658 (2007)CrossRefGoogle Scholar
 12.L. Musavian, S. Aissa, Fundamental capacity limits of cognitive radio in fading environments with imperfect channel information. IEEE Trans. Commun. 57(11), 3472–3480 (2009)CrossRefGoogle Scholar
 13.X. Kang, Y.C. Liang, A. Nallanathan, H.K. Garg, R. Zhang, Optimal power allocation for fading channels in cognitive radio networks: Ergodic capacity and outage capacity. IEEE Trans. Wirel. Commun. 8(2), 940–950 (2009)CrossRefGoogle Scholar
 14.R. Zhang, Y.C. Liang, Exploiting hidden powerfeedback loops for cognitive radio, in Proceedings of IEEE Symposium New Frontiers in Dynamic Spectrum Access Networks (DySPAN) (2008), pp. 1–5Google Scholar
 15.H.A. Suraweera, P.J. Smith, M. Shafi, Capacity limits and performance analysis of cognitive radio with imperfect channel knowledge. IEEE Trans. Veh. Technol. 59(4), 1811–1822 (2010)CrossRefGoogle Scholar
 16.G.J. Foschini, M.J. Gans, On limits of wireless communications in a fading environment when using multiple antennas. Wirel. Pers. Commun. 6(3), 311–335 (1998)CrossRefGoogle Scholar
 17.L. Zheng, D.N.C. Tse, Diversity and multiplexing: a fundamental tradeoff in multipleantenna channels. IEEE Trans. Inf. Theory 49(5), 1073–1096 (2003)zbMATHCrossRefGoogle Scholar
 18.F. RashidFarrokhi, L. Tassiulas, K.J.R. Liu, Joint optimal power control and beamforming in wireless networks using antenna arrays. IEEE Trans. Commun. 46(10), 1313–1324 (1998)CrossRefGoogle Scholar
 19.R. Zhang, Y.C. Liang, Exploiting multiantennas for opportunistic spectrum sharing in cognitive radio networks. IEEE J. Sel. Top. Signal Process. 2(1), 88–102 (2008)CrossRefGoogle Scholar
 20.R. Zhang, F. Gao, Y.C. Liang, Cognitive beamforming made practical: effective interference channel and learningthroughput tradeoff. IEEE Trans. Commun. 58(2), 706–718 (2010)CrossRefGoogle Scholar
 21.F. Gao, R. Zhang, Y.C. Liang, X. Wang, Design of learningbased mimo cognitive radio systems. IEEE Trans. Veh. Technol. 59(4), 1707–1720 (2010)CrossRefGoogle Scholar
 22.M. Mohseni, R. Zhang, J.M. Cioffi, Optimized transmission for fading multipleaccess and broadcast channels with multiple antennas. IEEE J. Sel. Areas Commun. 24(8), 1627–1639 (2006)Google Scholar
 23.L. Zhang, Y. Xin, Y.C. Liang, H.V. Poor, Cognitive multiple access channels: optimal power allocation for weighted sum rate maximization. IEEE Trans. Commun. 57(9), 2066–2075 (2009)CrossRefGoogle Scholar
 24.L. Zhang, R. Zhang, Y.C. Liang, Y. Xin, H.V. Poor, On gaussian mimo bcmac duality with multiple transmit covariance constraints. IEEE Trans. Inf. Theory 58(4), 2064–2078 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
 25.L. Zhang, Y.C. Liang, Y. Xin, H.V. Poor, Robust cognitive beamforming with partial channel state information. IEEE Trans. Wirel. Commun. 8(8), 4143–4153 (2009)CrossRefGoogle Scholar
 26.E.A. Gharavol, Y.C. Liang, K. Mouthaan, Robust downlink beamforming in multiuser miso cognitive radio networks with imperfect channelstate information. IEEE Trans. Veh. Technol. 59(6), 2852–2860 (2010)CrossRefGoogle Scholar
 27.Y. Pei, Y.C. Liang, L. Zhang, K.C. Teh, K.H. Li, Secure communication over miso cognitive radio channels. IEEE Trans. Wirel. Commun. 9(4), 1494–1502 (2010)CrossRefGoogle Scholar
 28.Q. Xiong, Y.C. Liang, K.H. Li, Y. Gong, S. Han, Secure transmission against pilot spoofing attack: a twoway trainingbased scheme. IEEE Trans. Inf. Forensics Secur. 11(5), 1017–1026 (2016)CrossRefGoogle Scholar
 29.X. Kang, H.K. Garg, Y.C. Liang, R. Zhang, Optimal power allocation for ofdmbased cognitive radio with new primary transmission protection criteria. IEEE Trans. Wirel. Commun. 9(6), 2066–2075 (2010)CrossRefGoogle Scholar
 30.X. Zhang, D.P. Palomar, B. Ottersten, Statistically robust design of linear MIMO transceivers. IEEE Trans. Signal Process. 56(8), 3678–3689 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
 31.A. Paulraj, R. Nabar, D. Gore, Introduction to SpaceTime Wireless Commun (Cambridge University Press, Cambridge, 2003)Google Scholar
 32.S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004)Google Scholar
 33.B. Hassibi, B.M. Hochwald, How much training is needed in multipleantenna wireless links? IEEE Trans. Inf. Theory 49(4), 951–963 (2003)zbMATHCrossRefGoogle Scholar
 34.F. RashidFarrokhi, K.J.R. Liu, L. Tassiulas, Transmit beamforming and power control for cellular wireless systems. IEEE J. Sel. Areas Commun. 16(8), 1437–1450 (1998)CrossRefGoogle Scholar
 35.N. Jindal, S. Vishwanath, A. Goldsmith, On the duality of Gaussian multipleaccess and broadcast channels. IEEE Trans. Inf. Theory 50(5), 768–783 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
 36.W. Yu, T. Lan, Transmitter optimization for the multiantenna downlink with perantenna power constraints. IEEE Trans. Signal Process. 55(6), 2646–2660 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
 37.Yu. Wei, Uplinkdownlink duality via minimax duality. IEEE Trans. Inf. Theory 52(2), 361–374 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
 38.W. Zhi, YC. Liang, M.Y.W. Chia, Robust transmit beamforming in cognitive radio networks, in 2008 11th IEEE Singapore International Conference on Communication Systems (2008), pp. 232–236Google Scholar
 39.S.Y. Lien, K.C. Chen, Y.C. Liang, Y. Lin, Cognitive radio resource management for future cellular networks. IEEE Wirel. Commun. 21(1), 70–79 (2014)CrossRefGoogle Scholar
 40.S. Sadr, A. Anpalagan, K. Raahemifar, Radio resource allocation algorithms for the downlink of multiuser OFDM communication systems. IEEE Commun. Surv. Tut. 11(3), 92–106 (2009)CrossRefGoogle Scholar
 41.H. Zhang, L. Venturino, N. Prasad, P. Li, S. Rangarajan, X. Wang, Weighted sumrate maximization in multicell networks via coordinated scheduling and discrete power control. IEEE J. Sel. Areas Commun. 29(6), 1214–1224 (2011)CrossRefGoogle Scholar
 42.X. Lin, H. Viswanathan, Dynamic spectrum refarming with overlay for legacy devices. IEEE Trans. Wirel. Commun. 12(10), 5282–5293 (2013)CrossRefGoogle Scholar
 43.X. Lin, H. Viswanathan, Dynamic spectrum refarming of GSM spectrum for LTE small cells, in Proceedings of IEEE Globecom Int, Workshop on Heterogeneous and Small Cell Networks (2013)Google Scholar
 44.S. Verdu, S. Shamai, Spectrum efficiency of CDMA with random spreading. IEEE Trans. Inf. Theory 45(2), 622–640 (1999)zbMATHCrossRefGoogle Scholar
 45.M.G. Khoshkholgh, K. Navaie, H. Yanikomeroglu, Access strategies for spectrum sharing in fading environment: overlay, underlay, and mixed. IEEE Trans. Mobile Comput. 9(12), 1780–1793 (2010)CrossRefGoogle Scholar
 46.S.M. Almalfouh, G.L. Stuber, Interferenceaware radio resource allocation in OFDMAbased cognitive radio networks. IEEE Trans. Veh. Technol. 60(4), 1699–1713 (2011)CrossRefGoogle Scholar
 47.S. Han, Y.C. Liang, B. Soong, S. Li, Dynamic broadband spectrum refarming for ofdma cellular systems. IEEE Trans. Wirel. Commun. 15(9), 6203–6214 (2016)CrossRefGoogle Scholar
 48.S. Han, Y.C. Liang, B.H. Soong, Spectrum refarming for OFDMA small cells overlaying CDMA cellular networks, in Proceedings of IEEE ICCS, special session on Cognitive Cellular Networks, Macau (2014)Google Scholar
 49.J. Tan, Y.C. Liang, S. Han, G. Yang, Ondemand resource allocation for OFDMA small cells overlaying CDMA system, in Proceedings of IEEE Global Communications Conference (GLOBECOM) (2016), pp. 1–6Google Scholar
 50.3GPP technical specification group radio access network: physical layer general description, 3GPP TS 25.201 V10.0.0, 2014Google Scholar
 51.S. Han, Y.C. Liang, B. Soong, Spectrum refarming: a new paradigm of spectrum sharing for cellular networks. IEEE Trans. Commun. 63(5), 1895–1906 (2015)CrossRefGoogle Scholar
 52.S. Han, Y.C. Liang, B.H. Soong, Joint resource allocation in OFDMA/CDMA spectrum refarming system. IEEE Wirel. Commun. Lett. 3(5), 469–472 (2014)Google Scholar
 53.G. Bansal, M.J. Hossain, V.K. Bhargava, Optimal and suboptimal power allocation schemes for ofdmbased cognitive radio systems. IEEE Trans. Wirel. Commun. 7(11), 4710–4718 (2008)CrossRefGoogle Scholar
 54.A.G. Marques, X. Wang, G.B. Giannakis, Dynamic resource management for cognitive radios using limitedrate feedback. IEEE Trans. Signal Process. 57(9), 3651–3666 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
 55.S. Han, Y.C. Liang, B. Soong, Robust joint resource allocation for OFDMACDMA spectrum refarming system. IEEE Trans. Commun. 64(3), 1291–1302 (2016)CrossRefGoogle Scholar
 56.H. Claussen, L.T.W. Ho, L.G. Samuel, An overview of the femtocell concept. Bell Labs Tech. J. 13(1), 221–245 (2009)CrossRefGoogle Scholar
 57.V. Chandrasekhar, J. Andrews, Spectrum allocation in twotier networks. IEEE Trans. Commun. 57(10), 3059–3068 (2009)CrossRefGoogle Scholar
 58.W.C. Cheung, T.Q.S. Quek, M. Kountouris, Throughput optimization in twotier femtocell networks. IEEE J. Sel. Areas Commun. 30(3), 561–574 (2012)CrossRefGoogle Scholar
Copyright information
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.