## 2 System Model and Design Objective  
The assumed system model is based on the 3 GPP defined High Speed Packet Access (HSPA) system [1,10], assuming co-channel deployment of all cells on a single carrier of 5 MHz bandwidth. A regular hexagonal grid of three sector macro base station sites is assumed as shown in Figure 1, each having a downlink transmission power of 43 dBm per cell and a 14 dBi antenna gain. For the sake of simplicity, the MNBs are assumed to always transmit at their maximum power level with a constant transmit power for the primary common pilot channel (P-CPICH). In addition to the macro-layer, HNBs are deployed across the network area according to two basic deployment strategies: either in houses (suburban) or in apartments (dense urban). This system model provides some variability due to its indoor propagation model (based on indoor distance and internal walls). Moreover, the shadowing model ensures that there is variance between the effective propagation loss a femtocell connected user experiences to the nearest macro base station and the estimated propagation loss using the NLM method at the HNB. Each HNB is serving a single cell with two 0 dBi omni directional antennas. The maximum HNB transmission power is assumed to be 15 dBm. Via NLM operation, the HNB is able to perform measurements in the downlink transmission band, including (i) received signal strength indicator (RSSI); and (ii) received signal pilot code power (CPICH RSCP) from other transmitting cells in the vicinity [11]. Serving cell selection for each UE is based on UE measurements of RSCP, _i.e._, the UE connects to the cell with strongest RSCP. A UE connected to an HNB is denoted an HUE and a UE connected to a MNB is denoted an MUE. When simulating with CSG HNBs, only UEs with matching CSG identity are allowed to connect. In this context, we consider any UE within an apartment or a house with an HNB to be part of the CSG, whereas any user outside of this space is unable to access the HNB. In the OSG case, there are no restrictions. We include common channels such as the P-CPICH, the high speed shared control channel (HS-SCCH), as well as the high speed downlink shared channel (HS-DSCH) in our modeling. The HS-DSCH is a time-domain shared channel with hybrid automatic repeat request (H-ARQ) and fast modulation coding, ranging from QPSK with high effective coding rate to 64 QAM with low effective coding rate. Assuming up to 15 high speed physical downlink shared channel (HS-PDSCH) codes, the maximum downlink data rate equals 21.1 Mbps [1]. Each UE is assumed to be equipped with two uncorrelated receive antennas, using a standard linear minimum mean square error (MMSE) receiver. The packet scheduling is round robin type. For more information on downlink fast link adaptation and packet scheduling, the reader is referred to [1, 12, 13]. Contrary to the downlink, the uplink uses dedicated channel transmission for each UE with fast closed loop power control with a 1.5 kHz command rate. The maximum UE transmission power equals 24 dBm, with the possibility for the network to configure lower maximum output power for some UE (also known as configuration of UE power capping) e.g., HUEs. Uplink reception is based on two receiver antennas with MMSE. The uplink packet scheduler is a standard best effort [1]. For the MNB, the scheduling is furthermore subject to a maximum uplink noise rise (NR) target, as well as minimum data rate per user. The NR is defined as the total received power divided by the thermal noise power [1], assuming a NR target of 6 dB for the MNB. The overall design objective is summarized in Figure 2. for a simple example with co-channel deployment of MNBs and HNBs, each serving one user. The objective is to adjust the HNB transmit powers of P-CPICH and HS-DSCH, as well as the HUE maximum transmit power, subject to the desired design criteria.