In this section, we categorize the related work about the beamforming and/or schedul-ing design for the sum rate maximization and transmit power minimization in the hierarchical underlying CR systems. The works of [5] and [9] focused on the trans-mit power minimization in the hierarchical underlying CR systems. The work [5]
proposed a joint beamforming and power control algorithm to minimize the transmit power of secondary system under the constraint that the QoS requirement must be satisfied. However, the channel information between primary BS and users is difficult to obtain at a secondary BS since the cooperation between the primary and secondary users are required. In [9], the interference power constraint of the primary system was satisfied instead of the QoS constraint of the primary users. The work [9] proposed two suboptimal algorithms based on the least square and admission control.
The works [6–8] focused on the sum rate maximization. The work [6] proposed
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a suboptimal joint beamforming and scheduling algorithm based on zero forcing beam-forming with equal power allocation and channel correlation between the primary and secondary users. However, the constraint of interference power to the primary system can not be satisfied in some cases. The work [7] develops a joint beamforming and power control iterative algorithm to sum rate maximization for fixed given serving set. However, the algorithm is only suitable in high SINR regime, which is not rea-sonable in interference-limited environment. A joint zero-forcing beamforming and user scheduling algorithm is proposed [8] to mitigate the the cross-tier interference.
The scheduling in [8] includes both the primary and secondary users, but it is not practical for the primary users scheduling in the underlay CR systems. We compare our work with above research in Table 2.1.
Based on the above discussions, we can summarize that the problem of joint power allocation, beamforming and scheduling design to maximize the sum rate of the secondary CR system under the interference constraint has not been investigated well.
Table 2.1: Literature Survey
Power Control Beamforming Scheduling Note
[5]
Joint design by weighted
x
Manage interference by least square suboptimal inactivating secondary users.
[6] Equal power Zero forcing Orthogonality
Not guarantee the interference constraint
[7]
Joint design by
x Capacity approximation convex optimization
[8] x Zero forcing Orthogonality
Joint primary and secondary users scheduling.
Our works Joint design by 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 has a licensed spectrum. The secondary system is a multi-user broadcast system, which 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 sec-ondary 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 systems. Second, in order to cancel the interference, the channel state information (CSI) must be known at the secondary BS for utilizing downlink spectrum. In gen-eral, the CSI to the primary BS is more easily obtained than CSI to primary users.
Primary
Figure 3.1: Spectrum usage of hierarchical CR system with FDD primary system and TDD/FDD secondary system.
as shown in Fig. 3.2. Since the CSI between the primary and the secondary users are also required, TDD secondary system shown in Fig. 3.2(b) is preferable for the pur-pose of feedback. To summarize, FDD primary system and TDD secondary system utilizing the primary uplink spectrum is considered in the thesis.
The hierarchical underlying CR system with FDD primary system and TDD secondary system is shown in Fig. 3.3. For simplification, assumes that only one primary utilizes the uplink band at a time. The primary BS, primary users and the secondary users are equipped with single antenna. The secondary BS are equipped with M . The secondary BS serve M secondary users at the most, which is selected
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Secondary DL Secondary UL
t f
Primary UL
t f
Primary DL
(a) FDD secondary system
t f
Secondary Primary UL DL
t f
Primary DL
Secondary DL Secondary
UL
(b) TDD secondary system
Figure 3.2: Spectrum usage of hierarchical CR system with TDD primary system and FDD/TDD secondary system.
from K secondary users, where K > M . Both frequency non-selective and frequency selective fading channel are considered in the next section.
Primary system
Secondary system
g0
g1
g2
gK
h1
h2
hK
Data Interference
Figure 3.3: Hierarchical cognitive radio networks with a FDD primary system and a TDD secondary system, where the downlink spectrum of the secondary system utilizes the uplink spectrum of the primary system.
3.1 Single Carrier Hierarchical Cognitive Radio Sys-tem
For a frequency non-selective channel, there is no inter-symbol interference (ISI).
Thus, we may process the transmitted signal in the time domain, where sk and x denote the transmitted signals from the secondary BS to the kth secondary user and the primary user to primary BS, respectively. An M × 1 vector wk represents beamforming weight for the kth secondary user. S is the set of served users, where
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S ⊆ {1, · · · , K}. The received signal of kth secondary user is
where hk denotes channel between M antennas of a secondary BS and the kth sec-ondary user,√
Q denotes the transmit power of the primary users, gk denotes channel between primary user and kth secondary user, and nk is a Gaussian noise for kth sec-ondary user with zero mean and variance σN2. We assume that the average power of signal E[
|sk|2]
is normalized to one. Thus, the transmission power to the kth users is ∥wk∥2. In addition, the received signal at the primary BS can be written as
r0 =√
where n0 is the noise at the primary. Here, h0 represents channel between all the served secondary users and the primary BS, g0 represents channel between primary BS and primary user, and can be expressed as
gk= αkak, k = 1, ..., K (3.3)
hk= βkbkvk, k = 0, ..., K (3.4) where αk and βk are the long-term fading, which includes pathloss exponent of four, and log-normal shadow with standard deviation of 8 dB; ak and bk are short-term Rayleigh fading, Note that vk is the steering vector which represent the relative phase at each antenna
vk=[
1, ejϕk,· · · , ej(M−1)ϕk]T
(3.5) where ϕk depends on the carrier frequency and propagation direction of the plane wave.
For a hierarchical CR system, the interference to the primary system should be limited strictly. Therefore, we design beamforming weights to control the inter-cell interference (ICI) shown in (3.2) to be lower than a pre-defined threshold, while minimizing intra-use interference (IUI).