Arrays and Power Ratio Adjustments
7.2 The Hierarchical CDMA System Model
7.2.1 System Description
As shown in Fig. 7.1, our hierarchical CDMA system consists of K + 1 overlaying FDD mode CDMA macrocells and one TDD mode CDMA microcell underlaid to the center macrocell with distance d. Let the cell M or the cell 0 denote the center macrocell and the cell µ denote the microcell. Then let RM and Rµ be the radius of the macrocell and the microcell, respectively. Assume that in each macrocell and microcell, NM and Nµ users are uniformly distributed, respectively. The mobile in the microcell is assumed to operate in TDD/CDMA mode and shares the uplink frequency of the overlaying FDD/CDMA mode macrocells. Therefore, there exists four types of interference between the heterogeneous system as shown in Fig. 7.2:
1. Interference from a macrocell mobile station (MS) to a microcell base station (BS);
2. Interference from a microcell MS to a macrocell BS;
3. Interference from a microcell BS to a macrocell BS;
(Base station-to-Base station co-channel interference) 4. Interference from a macrocell MS to a microcell MS.
(mobile-to-mobile co-channel interference)
The type 3 and type 4 interference result from the frequency sharing between the heterogeneous system. To alleviate the mutual interference between the microcell
and the macrocells, we propose to employ the AA at the cell site and the PRA technique.
Figure 7.1: The hierarchical CDMA system model.
Figure 7.3 shows the frame structure of the TDD/CDMA system. There are SU uplink time slots and SD downlink time slots in a frame. We assume each mobile in the TDD/CDMA microcell uses one uplink time slot and SD/SU downlink time slots for traffic asymmetry. Let Ns = dNµ/SUe denote the number of used codes per time slot. And let the {SU(i − 1) + j}-th mobile (i = 1, · · · Ns, j = 1, · · · SU) be sequentially allocated to the j-th uplink time slot in one frame. Therefore, for the microcell base station, there are NS code channels receiving over SU slots and transmitting over SD slots in each frame, respectively.
Figure 7.2: Mutual interference in the hierarchical CDMA system.
For clarity, we will use the notations in the following manners. When M and µ are used as either superscripts or subscripts, they denote the center macrocell and the microcell respectively. U and D represent the uplink and downlink respectively. And r and t are used as superscripts to denote the receiving and transmitting respectively from the base station. For example, Po,MU denotes the uplink outage probability of the macrocell, and Po,µD for the downlink outage probability of the microcell.
7.2.2 Power Ratio Adjustments
We assume ideal power control in the uplink. Let PMr and Pµr denote the received power level controlled by the base station of the macrocell and microcell, respectively.
Figure 7.3: Frame structure of the TDD/CDMA system.
Here, we define the first power ratio adjustment K1 as K1 = Pµr
PMr . (7.1)
It will be seen in Section 7.3 that the adjustment of the K1 can be used to balance the influence of type 1 and type 2 interference.
The link gain G(r, α) between the transmitter and the receiver with distance r is modelled by propagation loss and lognormal shadowing
G(r, α) = min(κ0r−m· 10α/10, (MCL)) . (7.2) where κ0is a constant, m is the path loss exponent and α is a normal random variable with zero mean and standard deviation σ dB. Otherwise, we introduce minimum
coupling loss (MCL) as the minimum distance loss including antenna gain measured between antenna connectors [46]. The value of σ and MCL are different with the distinct environment conditions. We assume that MCL between base station and mobile is equivalent to 10−5.3 and MCL between base station and mobile is equal to 10−4 [47].
Let Pµt denote the transmitted power from the base station for each mobile in the microcell. After propagating over a distance of the cell radius, the received signal power at the boundary of the microcell equals Pµt· (κ0Rµ−m) without considering the lognormal shadowing. Therefore, we define the second power ratio adjustment K2 as
K2 = Pµt
PMr · (κ0Rµ−m) . (7.3)
In the following section, we will show that the adjustment of K2, when combined with the AA, is effective to cope with the type 4 interference without aggravating type 3 interference.
7.2.3 Antenna Array and Beamforming
In this chapter, we propose that the L-element uniform circular array (UCA) is adopted at both macrocell and microcell sites to enhance signal-to-interference ratio by using uplink and downlink beamforming. Assume the narrowband siganl model and perfect power control in the uplink. If aij is the L × 1 receiving array response vector for the signal arriving from the mobile j, the received interference power from the mobile j for the desired mobile i at the cell site (e.g. the macrocell M) is given by
Iij = PMr kwiHaijk2 . (7.4) where H is the Hermitian transpose operation, k · k is the norm operation and wi is a L × 1 weight vector to combine the output of L-element antenna array. Similarly,
if ˜wi is a L × 1 transmitting weight vector for the desired mobile i, bij is the L × 1 transmitting array response vector of the mobile j seen by the base station (e.g. the microcell µ), the received interference due to leakage from the transmitted power of the base station to the mobile j is given by
Iij = Pµtk ˜wHi bijk2 . (7.5) There are several ways to derive the weight vector under different criterions.
We adopt the maximum ratio combining (MRC) in this chapter. As a result, the receiving weight vector is equal to its receiving array response vector [35]. Moreover, thanks to the channel reciprocity in TDD system, the weight vector obtained in the uplink can be applied to the downlink beamforming provided that the channel remains stationary between uplink and downlink during a time frame [57].
7.2.4 Bit Energy-to-Noise Density Ratio of FDD Cells
Now, we can obtain the uplink bit energy-to-noise density ratio of the mobile i in the center macrocell. By neglecting the thermal noise, from [52] (Eb/N)UM,i is given by
µEb
From (7.7) to (7.9), P GM is the processing gain for the macrocell, ψj is a Bernoulli variable with probability v to model the voice activity, rj(k) is the distance between the mobile j and the base station k, α(k)j is the path shadowing between the mobile j and the base station k, a(k)ij is the receiving array response vector for signal arriving from the mobile j in the cell k. Thus, I1 denotes the intracell interference from the mobiles in the center macrocell, I2 denotes the intercell interference from the mobiles in adjacent macrocells, and I3 denotes the type 2 intersystem interference. When the base station in the microcell is transmitting instead of receiving, the intersystem interference turns out to be the type 3 interference I30, which is given by
I30 =
Ns
X
j=1
PµtG(d, α)k ˜wHj bk2kwHi ak2 . (7.10) where a is the receiving array response vector for signal arriving from the microcell base station, b is the transmitting array response vector for signal transmitting from the microcell base station to the macrocell base station, and ˜wj is the transmitting weight vector for any mobile j in the microcell.
7.2.5 Bit Energy-to-Noise Density Ratio of TDD Cells
In the following, we derive the uplink and downlink bit energy-to-noise density ratio of the TDD microcell. For the desired mobile i in the microcell, the uplink bit energy-to-noise density ratio of the microcell can be obtained as
µEb
is the intracell interference from the mobiles in the microcell and is the type 1 interference from the mobiles in the macrocells.
On the other hand, when the mobile i in the mircocell is receiving, the inter-ference then comes from I1 and I2. I1 in this case denotes the interference from the microcell base station and I2 denotes the type 4 intersystem interference. Thus, the downlink bit energy-to-noise density ratio of the microcell can be obtained as
µEb In (7.14)-(7.16), rji and αij are the distance and the path shadowing between the desired mobile i in the microcell and other mobile j in the macrocell, respectively.