Time division duplex (TDD) is a duplex scheme where both uplink and downlink traffic takes place in the same unpaired frequency band. By allocating different numbers of slots for uplink and downlink, the TDD system can support asymmetric traffic services with great flexibility [68, 69]. Another merit of the TDD system over the frequency division duplex (FDD) system is the channel reciprocity that can be exploited to implement, for example, efficient open-loop power control [68, 70], pre-equalization [71, 72] and pre-rake diversity technique [73, 74]. With these advantages, modern cellular standards such as [75]
have incorporated the TDD mode into their system designs.
2.3.1 Opposite Direction Interference
Despite the advantage of flexibly supporting traffic asymmetry in the TDD system, the TDD/CDMA system may pose a severe opposite direction interference problem across cells due to the universal frequency reuse of CDMA [6]. Figure 2.6 illustrates the typical in-terference scenario in the TDD/CDMA system. Assume that cells A and B in the figure have different rates of traffic asymmetry and allocate time slots independently according to their own traffic requirements. During a particular time slot to, one can find that the uplink received signals at cell A may suffer strong interference from the downlink transmitted sig-nals of the neighboring cell B. In this dissertation, we call this kind of base stations to base stations interference the opposite direction interference because the desired signal is in the uplink direction, while the interference is from the downlink direction.
On the other hand, in time slot ts of Fig. 2.6, the uplink transmissions from the users in cell B will interfere with the uplink signals of cell A. We call this kind of mobile stations to base stations interference the same direction interference. The same direction interference also occurs in FDD/CDMA systems. Many previous works, such as [76, 77], have analyzed
Cell A Cell B
(1) : Opposite direction interference from cell B to cell A (2) : Same direction interference from cell B to cell A
(1) (2)
downlink uplink
uplink
U : uplink time slot D : downlink time slot
D D D U U U
D D D D U U
(1) (2)
Cell A
Cell B
t
ot
sFigure 2.6: Opposite direction interference in the TDD/CDMA system.
the impact of the same direction interference. Thanks to power control mechanisms and other techniques, the impact of the same direction interference can be effectively managed in FDD/CDMA systems. However, the opposite direction interference, which is unique in TDD/CDMA systems, is substantially different from the same direction interference. First, it is difficult to coordinate many base stations throughout the entire service area to perform downlink power control simultaneously. Moreover, since the transmitter power of a base station is much higher than that of a mobile station, the opposite direction interference introduced by the neighboring base stations will severely degrade the quality of uplink signals transmitted from a mobile station [6, 78].
Usually, to avoid the opposite direction interference in TDD/CDMA systems, one can use different frequency carriers among adjacent cells. Obviously, this approach sacrifices frequency reuse efficiency. To use the same frequency carriers in every TDD/CDMA cell, one possible solution to avoid the opposite direction interference is to restrict all the neighboring
cells to adopting the same slot allocation pattern [79], i.e., all the assignments for either uplink or downlink transmissions in every time slot are the same. However, this approach implies that all cells will be forced to adopt the same rate of traffic asymmetry in the entire system, which is obviously not a very practical restriction. The key to relax this restriction is to overcome the opposite direction interference in the TDD/CDMA system. In the literature, there are two research directions to avoid the opposite direction interference:
• The first research direction is from the perspective of channel assignment techniques, such as [17, 18]. In [17], Haas and McLaughlin proposed a dynamic channel assign-ment algorithm to reduce the occurrence of the opposite direction interference due to asymmetric traffic. However, the authors in [18] concluded that it may be difficult to achieve the optimal time slot allocation in an environment with multiple TDD/CDMA cells.
• Another research direction to alleviate the impact of the opposite direction interference in TDD/CDMA systems is to apply the multiple antenna technique [19, 20, 21]. The authors in [19] and those in [20] proposed to adopt sector antennas combined with time slot allocation methods to suppress the opposite direction interference for the TDD/CDMA system and for the TDD/TDMA system, respectively. Furthermore, it was shown in [21] that the diversity-based SC and MRC antenna schemes are not feasible to resolve the opposite direction interference issue for the TDD/CDMA system.
In Chapter 6, we will investigate the effect of using the antenna beamforming technique to resolve the opposite direction interference in the TDD/CDMA system.
Chapter 3
Fading Mitigation Based Antenna Techniques for Multiuser Scheduling Systems
In this chapter, we develop an analytical framework to study the interaction between the fading mitigation based (or diversity-based) antenna technique and the multiuser scheduling system. We consider a multiuser scheduling system as described in Section 2.2. Under the generalized Nakagami fading channel model, we will derive a unified capacity formula applicable for the multiuser scheduling system with a number of fading mitigation based antenna schemes, including
• Selective transmission/selective combining (ST/SC), standing for that the selective transmission and selective combining schemes are utilized at the transmitter and the receiver, respectively.
• Maximum ratio transmission/maximum ratio combining (MRT/MRC).
• Selective transmission/maximum ratio combining (ST/MRC).
• Space-time block codes (STBC).
With a further change of parameters, the derived capacity formula can be versatile to inter-pret the interplay of antenna diversity and multiuser scheduling within the multiuser MIMO network.
3.1 Channel Model
To investigate the impact of channel fading on the multiuser scheduling system, this chapter considers the generalized Nakagami fading channel model. Consider a multiuser scheduling system with a base station serving K downlink users as shown in Fig. 2.5. To begin with, we assume that the base station and each user have only one single antenna. Let hk be the channel gain between the base station and user k, and let σn2 be the thermal noise power.
Accordingly, γk = |hk|2/σn2 denotes the received instantaneous SNR of user k. We assume that each link between the base station and any user is subject to independent Nakagami fading with a common Nakagami fading parameter m. Then, the probability density function (PDF) of the received SNR for user k is [24]
fγk(γ) =
where ρk is the average received SNR, and Γ(·) is the gamma function defined by
Γ(m) =
∞
0
tm−1e−tdt . (3.2)
When m = 1, the Nakagami fading channel is identical to the Rayleigh fading channel. For m > 1, a line-of-sight or a specular component exists. As m → ∞, the Nakagami channel approaches to the AWGN channel.
To ease notation, we denote X ∼ G(p, q) as a gamma distributed random variable with parameters p and q. Then, the PDF of X is given as [80]
fX(x) = qp
Γ(p)xp−1e−qx, x > 0 . (3.3) Furthermore, the cumulative distribution function (CDF) of X can be expressed by
FX(x) = Γ(p, qx) , (3.4)
where Γ(·, ·) is the normalized incomplete gamma function defined by [82]
Γ(a, x) = 1 Γ(a)
x 0
ta−1e−tdt . (3.5)
Based on the above notation, the distribution of γkin the Nakagami fading channel model can be represented by γk∼ G
m,ρm
k
. Next, we introduce two lemmas regarding the properties of gamma random variables, which will be used in Section 3.3.
Lemma 3.1 Let X1, X2,· · · , XK be independent gamma random variables with parameters pk and q, respectively. Let Y be the random variable given by Y = X1+· · · + XK. Then we have
Y ∼ G
K
k=1
pk, q
. (3.6)
Proof: Please refer to [80].
Lemma 3.2 Let X be a gamma random variable with parameters p and q. Let Y be the random variable given by Y = cX, c > 0. Then we have
Y ∼ G p, q
c
. (3.7)
Proof: The proof is completed by using a simple variable transformation fY(y) = fX(y/c)/c ∼ G
p, qc
.