6 7 8 9 10 11 12
SNR ρ (dB)
Capacity (nats/sec/Hz)
K=10 K=5 K=3 K=1
Line: analysis Marker: simulation capacity bound
Figure 5.4: Capacity of the (MT = 2, MR= 3, K) receive ZF MIMO broadcast systems with different number of users K under ²2e = 1%.
and ²2e = 15% as K increases to 30 and 210, respectively. Although, it may be difficult for a system with enough user population (e.g. K = 210) to recover the reduced coverage.
This numerical example provides the potential gain of multiuser diversity on soft coverage extension.
5.4.2 Effects of Imperfect CSI-R on Sum Rate
Figure 5.3 presents the sum-rate capacity of a (MT = 2, MR = 3, K = 5) receive ZF MIMO broadcast systems with ²2e = 0, 1%, 5%, and 10% by simulative and analytical ways. Clearly, the sum rate will increase linearly as SNR ρ increases in dB under no estimated error con-dition. Different from the effect of feedback error on sum rate discussed in Chapter 3, the imperfect CSI-R will largely drop down the sum rate of the receive ZF MIMO broadcast
−10 −5 0
0.2 0.4 0.6 0.8 1 1.2 1.4
SNR ρ (dB)
Capacity (nats/sec/Hz)
0 5
0 1 2 3 4 5 6
SNR ρ (dB)
Capacity (nats/sec/Hz)
Equal power (simulation) Equal power (analysis) Water filling (simulation) Water filling (analysis)
Figure 5.5: Capacity comparison of the (MT = 3, MR = 4, K = 10) receive ZF MIMO broadcast systems under equal power and water-filling power allocations.
systems. More serious estimation error leads to more depressed sum rate performance. The resulting sum rate will no longer increase as SNR ρ increases and tend towards the value CZFR²2e
provided in (5.25). For example, the sum rate of the (2, 3, 5) receive ZF MIMO broadcast systems with ²2e = 0 is 15 nats/s/Hz at SNR ρ = 30 dB. However, the corresponding sum rates reduce to 10.38, 7.28, and 6.04 nats/s/Hz for ²2e = 1%, 5%, and 10%, respectively.
Next, we want to answer what advantage can multiuser diversity reflect on sum rate for a receive ZF MIMO broadcast system with imperfect CSI-R. Fig. 5.4 shows the sum rate of the receive ZF MIMO broadcast systems with MT = 2, MR = 3, ²2e = 1% and different number of users K. In this figure, the sum-rate performance can be improved as available user population K increases, but it can not be raised any more as SNR ρ approaches to about 35
dB. In fact, multiuser diversity can not resolve the sum rate floor caused by imperfect CSI-R.
The corresponding CZFR²2e values are 8.73, 9.98, 10.38, and 10.82 nats/s/Hz for K = 1, 3, 5, and 10, respectively.
Finally, we illustrate the benefit of utilizing water-filling power allocation on sum-rate performance via Fig. 5.5 which evaluates a (MT = 3, MR = 4, K = 10) receive ZF MIMO broadcast system. This figure confirms the well-known information that the advantage of water-filling power allocation over equal power allocation is significant only in the low SNR region. As shown, our provided closed-form expressions can well evaluate the sum-rate performance of the receive ZF MIMO broadcast systems under both equal and water-filling power allocations.
Chapter 6
Architecture for Coordinated Multicell MIMO Systems
In this chapter, we present a 3-cell network MIMO architecture with FFR and a novel tri-sector frequency partition scheme. One fundamental question to apply the network MIMO technique in such a high interference environment is: how many base stations should be coordinated together to provide sufficient performance? We will demonstrate that the FFR-based 3-cell network MIMO architecture with the proposed tri-sector frequency partition can not only effectively overcome the inter-group interference, but can avoid executing the complex multi-base-station joint processing for a huge number of cluster of cells at all lo-cations. It will be shown that the proposed 3-cell network MIMO with the rearranged tri-sector frequency partition strategy can outperform the seven-cell network MIMO with omni-directional antennas. Various sector antenna architectures and the method for deter-mining the inner region of the FFR cell planning are also discussed and analyzed on top of the network MIMO system. We hope that this study can provide important insights into the design of the network MIMO systems from the perspectives of architecture and deployment.
6.1 System Model
We consider a cellular system with Ncell = 19 cells, where the center cell has two-tier neigh-boring cells. In the baseline case, each base station and each user has one single trans-mit/receive antenna. When the cellular system with three sectors is considered, we assume that each sector is equipped with one sector antenna. The gain pattern used for each sector antenna is specified as
A(θ)dB = − min
"
12 µ θ
θ3dB
¶2 , Am
#
, (6.1)
where A(θ)dB is the antenna gain at angle θ in decibels and θ ∈ [−180◦, 180◦] is the angle between a mobile user with respect to the main-beam direction of the considered sector
antenna. The 3 dB beamwidth θ3dB is the angle of which the antenna gain is 3 dB lower than the antenna gain at the main-beam direction, and the parameter Am = 20 dB is the maximum attenuation for the sidelobe.
For the transmitted signal xj from base station j, the received signal of mobile user k is written as
yk = hk,jxj+ X
i6=j, i∈I
hk,ixi+ nk , (6.2)
where hk,j and nk are the channel response between mobile k and base station j and the additive noise at the k-th mobile, respectively; and I is the set of interfering BSs for mobile k. The radio channel models considered in this chapter include the effects of Rayleigh fading, shadowing, and path loss. Specifically, we represent the channel response hk,j as
hk,j = αk,j
where αk,j and βk,j are the fast Rayleigh fading and shadowing between mobile k and base station j, respectively; dk,j and dref are the distance between mobile k and base station j and a reference distance between the center and the vertex of a cell, respectively; and µ is the path loss exponent. A(θk,j) is the antenna gain for mobile k with respect to BS j whose value is a function of θk,j based on (6.1) for the sectorized antenna and A(θk,j) = 1 for the omni-directional antenna.
Considering the above signal and radio channel models, we can represent the received SNR of mobile k from base station j as
SNRk,j = |αk,j|2βk,jA(θk,j) µdk,j
dref
¶−µ
Γ , (6.4)
where Γ represents the interference-free SNR defined as the SNR measured at the reference distance dref with only considering pass loss, and the noise power is normalized to unity.
The parameter Γ captures the effect of various channel and antenna parameters including transmit power, cable loss, transmit and receive antenna heights, thermal noise power, and other link budget parameters. For dref ∼= 1.1547 km, the reference SNR Γ = 18 dB for a base station-to-BS distance RB2B = 2 km macrocellular system with 30 Watts transmit power [118]. For mobile k of BS j, we can express its corresponding SINR as
γk,j = SNRk,j
1 + X
i6=j, i∈I
SNRk,i
. (6.5)
The corresponding channel capacity for each SINR value γk,j can be given by log2(1 + γk,j) bit/s/Hz. In this chapter, we consider the achievable capacity for various MCS considered in the standard [117]. For the considered MCSs {QPSK12, QPSK34, 16-QAM12, 16-QAM34, 64-QAM23, 64-QAM34}, the corresponding SINR requirements and the spectrum efficiencies are {6, 8.5, 11.5, 15, 19, 21} dB and {1.0, 1.5, 2.0, 3.0, 4.0, 4.5} bit/s/Hz, respectively.