## Uplink Power Control for MIMO-OFDMA Cellular Systems

### Rongzhen Yang and Hujun Yin

[Abstract]In this paper, we propose a novel uplink power control algorithm, SMST, for multiple-input multiple-output orthogonal frequency-division multiple access (MIMO-OFDMA).We perform an extensive system-level simulation to compare different uplink power control algorithms, including the FPC adopted in 3GPP LTE and LTE-Advanced. Simulations show that SMST adopted in IEEE 802.16m outperforms other algorithms in terms of spectral efficiency, cell-edge performance, interference control, and trade-off control between sector-accumulated throughput and cell-edge user throughput. The SMST performance gain over FPC can be more than 40%.

[Keywords] uplink power control; inter-cell interference; OFDMA; MIMO

**1 Introduction** Uplink power control is a critical feature of CDMA cellular systems. It is used to alleviate the near-far problem caused by intracell interference. The new generation of broadband wireless technologies, including WiMAX and LTE, are designed to provide higher bandwidth, higher peak throughput, and higher spectral efficiency [1],[2]. These wireless technologies are based on orthogonal frequency-division multiple access (OFDMA), in which all the uplink transmissions are orthogonal within one cell [3]. Therefore, intracell interference is minimal compared with technologies based on 3G CDMA.

Fourth-generation WiMAX and LTE wireless standards are designed to support up to 20 MHz channel bandwidth, high-order 4 × 2 and 4 × 4 multiple-input multiple-output (MIMO), and aggressive frequency reuse (reuse 1) to improve spectral efficiency and user throughput. Especially for cell-edge users, intercell interference is a significant problem caused by aggressive frequency reuse. Uplink power control is an important mechanism for controlling intercell interference and improving cell-edge user experience (UE), even in broadband wireless systems based on OFDMA[4]-[7]. As opposed to 3G, where closed-loop power control is typically used to control both intracell and intercell interference, the main objective of uplink power control in OFDMA-based systems is to control intercell interference [8],[9].

In this paper, we investigate control of uplink transmit power in order to maximize sector and cell-edge spectral efficiency. These are essential parameters for next-generation broadband wireless systems [10]-[13]. A simplified maximum-sector throughput (SMST) algorithm is proposed that maximizes sector throughput by adjusting uplink transmit power.

**2 Uplink Power Control Mechanisms**

2.1 Background

Power control has been studied extensively since the introduction of cellular systems. A power-control mechanism can be closed-loop power control (CLPC), open-loop power control (OLPC), or CLPC-OLPC combined power control. In CLPC, power control is centralized at the base station (BS). The mobile station (MS) provides feedback on link quality, and the BS calculates the uplink transmit power level for the MS and instructs the MS to transmit at that level. In OLPC, the MS measures link quality and calculates the uplink transmit power level (based on predetermined equations) in a distributed manner. The BS may influence the MS by adjusting certain parameters in the equation, but the BS does not directly control the MS transmit power.

2.1.1 CLPC

In a CDMA system, CLPC allows commands to be sent from the BS so that power can be quickly adjusted. In an OFDMA system, intracell interference is not significant, so adaptive modulation and coding (AMC) and hybrid automatic repeat request (HARQ) are used to provide fast link adaptation for the data channel. CLPC is mainly used for fixed-rate control channel when channel fading exceeds the power margin. In CLPC in the BS, the received signal quality is monitored and power-adjustment commands are sent.

2.1.2 OLPC

OLPC is mainly implemented in the MS. The MS measures downlink signal status, compensates the uplink path loss, and controls interference to neighboring BSs. With OLPC, the MS needs some static/semi-static configuration parameters to be signaled by the BS and does not require short-term inputs. This saves overall signaling overhead.

2.1.3 CLPC-OLPC Combined Power Control

In current 4G wireless standards, both CLPC and OLPC are combined to balance flexibility with signaling overhead. OLPC is mostly used to save signaling overhead.

2.2 Uplink Power Control Algorithms

Depending on the goal of the power control mechanism, the uplink power-control algorithm can be based on signal-to-noise ratio (SNR), signal-to-interference plus noise ratio (SINR), or Internet of things (IoT).

2.2.1 SNR-Based Algorithm

The goal of an SNR-based algorithm is to maintain the desired received signal strength in the BS. An SNR-based algorithm does not take into consideration the uplink-received interference power level. This type of algorithm is simple to implement and always convergent. Fractional power control (FPC) in LTE is an SNR-based algorithm.

2.2.2 SINR-Based Algorithm

The goal of an SINR-based algorithm is to maintain the desired received SINR level in the BS while taking into account the uplink interference power level. SMST used in IEEE 802.16m is an SINR-based algorithm that defines the desired received SINR goal for each MS and takes into account the measured downlink signal-to-interference ratio (SIR), uplink MIMO mode, and BS antenna configuration.

2.2.3 IoT-Based algorithm

The goal of an IoT-based algorithm is to maintain the desired uplink interference level in the BS. In general, an IoT-based algorithm can stabilize the interference level in the uplink to help control interference and modulation-coding-scheme (MCS) level estimation.

**3 Maximizing Throughput with Power Control**

3.1 System Modeling

Fig. 1 shows an uplink interference model for one MS in a typical MIMO-OFDMA cellular system.

At any time, the MS uses the uplink to transmit to its home BS and causes interference to neighboring BSs. To simplify the analysis, simple input simple output (SISO) is assumed, and the parameters for the model are

- Ps : The MS uplink transmission power (linear) of one data subcarrier at a given time;
- i: cell index. i = 0 is the home BS, and i = 1-N is the neighboring BSs;
- CLi : The instantaneous channel loss (linear) from MS transmitter to one receiving antenna of a BS;
- NIi : The noise-plus-interference level (linear) per subcarrier at a BS receiving antenna.

**3.2 Maximum Throughput Criteria** The aggregated cell throughput is

If we assume that all BSs occupy the same bandwidth, (1) can be modified:

For uplink power control of each MS, aggregated spectrum efficiency SE is prioritized as the target of the algorithm, which can be expressed as

To solve (3) for each MS, the following process is used:

1) PS is the transmission power of one subcarrier that is initialized to 0

2) A power increase, ΔPS , is assumed in order to calculate

i) SE gain : as the power increases, this is the spectrum efficiency gain that the MS can achieve in the home BS on the subcarrier.

ii) SE loss : as the power increases, this is the spectrum efficiency loss the MS inflicts on the neighboring BSs on the subcarrier.

3) SE gain and SE loss are compared

i) If SE gain > SE loss, PS = PS + ΔPS , go back to 2

ii) If SE gain ≤ SE loss, then the PS is optimum on the subcarrier for the MS.

This process is used to evaluate the SE gain and SE loss for each power increase of ΔPS .

At any time, when a power increase of ΔPS is assumed, the SE gain of the MS on the subcarrier can be obtained by

where

Combining (4), (5), and (6), SEgain can be expressed as

The SE loss on the subcarrier in one neighbor BSi (i = 1-N ) can be expressed as

where SINR (i ) Original = ,

Si is the received signal power on the

subcarrier of BSi , and is

the increased inference power caused by ΔPS.

From (8), the total SEloss on the subcarrier in all neighbor BSs can be expressed as

Therefore, the optimum power on the subcarrier can be calculated by increasing P S of the subcarrier by ΔPS steps from 0 until the SE gain and SE loss on this subcarrier no longer satisfies

If the MS is assigned resources for uplink transmission by the BS, optimal transmission power for all assigned uplink subcarriers can be calculated in order to achieve the overall optimum cell throughput. This algorithm is called the maximum sector throughput (MST) algorithm.

**4 Simplified Maximum Sector Throughput Algorithm**

4.1 MST Algorithm Simplified Form

The MST algorithm is only useful in theory and is impossible to be implemented in practice. The algorithm requires the home BS or MS to accurately know the received signal power and interference power on all neighbor BSs on each subcarrier at the time of uplink transmission. Making some simple assumptions, we developed a practical SMST algorithm. First, we modeled one virtual neighbor BS (or sector) that accounts for all interference impact on SEloss (Fig. 2).

We assume that all BSs have the same downlink transmission power level. The total downlink reference interference power from the virtual BS to the MS is

where PDL_Preamble is the downlink preamble power used as the reference signal to measure downlink path loss, and CL I is the virtual downlink path loss. The downlink reference signal power of the MS is

Downlink SIR can be measured as

SIRDL = , so that

The SE gain can be expressed as

One virtual neighbor model is used, and one MS keeps the same transmission power spectral density (PSD) for all data tones (PSD Data). Only one transmission stream is used, and there are Nr receiving antennas at the BS (an MRC receiver is assumed).

It is further assumed that each receiving antenna on the BS suffers similar noise and interference level NIH,Ant , and the path loss from transmission antenna to each receiving antenna is similar to CLH , then (14) can be re-written as

Similarly, the new SE loss on the virtual neighbor BS can be expressed as

where NI I,Ant , is the noise plus interference for each antenna on the virtual BS, PNoice,Ant , is the white noise for each antenna on the virtual BS, SNR I,Ant is the average SNR level for each antenna on the virtual BS, and SNR I,Ant × PNoise,Ant , is used to estimate received signal PSD for each antenna on the virtual BS.

The optimum overall SE can be obtained when the following condition is met:

From (13), (15), (16) and (17), we can derive

where, SINR H,Ant is the received average SINR for each antenna on the home BS, and

Equation (18) can be further simplified:

where γ is a derived parameter to control the interference to other cells:

The parameter,γ , is linearly related to the ratio of virtual-cell average NI level to home-cell average NI level. High γ results in high interference over thermal (IoT), and low γ results in low IoT.

4.2 Limitation of Minimum Transmission Rate

Equation (19) provides the optimal solution for the SMST algorithm. The resulting target SINR on each antenna is expressed as a linear value. From (19), some MSs could have negative target SINR because of the very low measured downlink SIR. For these MSs, the results of (19) indicate that any power assigned to these MSs reduces overall throughput. Because all active MSs must support a minimum transmission rate to keep them online, the minimum target SINR (to support the minimum transmission rate) should be set as the threshold. Then, (19) is modified as follows:

In (21), the resulting target SINR is converted to decibels so that the transmission power can be conveniently calculated. The minimum SINR threshold is expressed in decibels and is converted into a linear value to align with the linear result of (19). Equation (21) is a core part of the IEEE 802.16m [3] uplink power-control algorithm.

Equation (21) is the SMST algorithm combined with minimum target SINR threshold. It expresses the suitable uplink target SINR in each receiving antenna on a home BS. If OLPC is applied, the PSD of each data subcarrier used by the MS is

where L is the average downlink path loss measured by MS base on BS transmission power level and received signal power level, NI is the average noise and interference level for each subcarrier at the BS antenna, the information is broadcasted from BS to MS, and Offset is the MS-specific power offset decided by the BS.

If (21) is used for conventional CLPC design, MS needs to report the measured downlink SIR value SIRDL to BS periodically, and BS then uses (21) to calculate the target SINR. Compared with the measured SINR, the difference is compensated by CLPC commands.

Equation (21) is the solution for uplink single stream. In IEEE 802.16m [11], two options for uplink multistream power control were discussed. The power level of each stream in uplink multistreams can be kept the same as the single stream or the power level of each stream in uplink multistreams can be reduced to keep the sum of

power/interference similar to the single stream. Both options improve performance in different cell sizes and in different scenarios, so there is one additional control parameter added into (18) to support both options:

where β is the newly added parameter and can be set by the BS as 0 (disabled) or 1 (enabled) for environment performance tuning. TNS is the total number of uplink multistreams.

Equation (23) is the final derivation of SMST adopted into IEEE 802.16m [3] for data-channel power control. 16 m control-channel power-control design was discussed in [14].

**5 Algorithm Evaluation and Comparison**

5.1 Evaluation Considerations

Before evaluating uplink power control algorithms, the following general points for system-level simulation need to be considered:

- sector-cumulated throughput and cell-edge throughput. These are the metrics of overall performance determined by uplink power-control algorithms.
- fairness control curve. In general, the uplink power control algorithm provides a trade-off between sector-cumulated throughput and cell-edge throughput. One new-form curve is used to show the sector SE and cell-edge SE (Figs. 3, 4, 8 and 9).
- IoT control. IoT is the key metric of uplink interference in a system evaluation. Effective IoT control needs to be proven for an uplink power control algorithm.

As (22) and (23) show, there are some key parameters that need to be evaluated and discussed for real implementation:

- γ plays a key role in IoT and fairness. In the evaluation, the results of different γ values are discussed
- SINR MIN (dB) is the minimum threshold for cell-edge user SINR.
- L is the average downlink path-loss measured by the MS. This is key to deciding the transmission power level. For different product implementations, the long-term average or short-term average have cause different effects.
- The open-loop power adjustment is decided by the MS. The rate of power control may be used in product implementation. Fast (per-frame) or slow (per 50 frames) control rates are evaluated.

5.2 Results and Discussion

The evaluation scenario in [15] follows the IEEE 802.16m Evaluation Methodology Document [16], but some simplifications are made for uplink power control. The key parameters of the evaluation scenario are listed in Table 1.

In the OLPC algorithm, path loss and power control rate are related to implementation. The path loss L is applied to (22) to calculate the transmission power for each subcarrier. L is estimated by the MS through downlink signaling measurement. For the extreme evaluation setting, the path loss L is assumed with two conditions:

- instantaneous path loss. This is the ideal accurate instantaneous (current frame) downlink value used in the simulation
- average path loss. This is the estimated path loss is the very long-term (~50 frames, smoothing factor = 0.02) average downlink path loss. Ideally, short-term fast fading is smoothed.

In product implementation, the path loss for a specific product should be somewhere between the two extremes, depending on the averaging factor. The SINR MIN (dB) is set as 0 dB, and the results are shown in Table 2.

With different γ values, the performance trade-off between sector SE and cell-edge SE is shown in Fig. 3 based on the results of Table 2.

For OLPC, the power adjustment rate based on (22) can be per frame (rate = 1) or infrequent (rate > 1). In general, the power control rate is assumed to be 1; that is, in each frame, OLPC is applied for uplink transmission. However, there are some parameters related to product implementation, such as path loss, L , and downlink signal versus interference SIR DL measurement and estimation. NI updating, broadcast by the base station, is not performer per frame. The change of power dictated by OLPC may be longer than one frame. Therefore, in one extreme case, a control rate of 50 frames is also simulated to verify the robustness of the SMST algorithm.

In Fig. 3 and Fig. 4, the robustness of SMST compared with path-loss estimation and power updating rate is very clear. The average path loss shows minor gain in sector average throughput but minor loss in cell-edge SE. The reason is that the estimated average path loss can help the MS maintain stable transmission power that is determined by OLPC. Then, the signal/interference estimation on the BS is more accurate, and this is very important for the adaptive and modulation coding (AMC) process to assign the desired MCS level to the MS. The average path loss shows minor loss in a cell-edge SE because instantaneous path-loss estimation allows the MS to perform fast-link adaption by OLPC power change. Similarly, Fig. 4 shows that a slow power-updating rate of 50 has some gain in maximum sector SE and some loss in cell-edge SE.

Other aspects of uplink power control, such as user throughput distribution, IoT control, and power distribution, are shown in one of the following four cases, because it is closely related to real product implementation. The evaluation results are presented as an empirical cumulative distribution function (CDF).

Fig. 5 shows one example of how the control factor,γ, controls the trade-off between sectors to accumulate throughput and fairness in cell-edge performance.

The IoT distribution shows the effectiveness of interference management.

Fig. 6 shows the relationship between IoT distribution and control factor γ. When γ = 0, the SMST algorithm degenerates to a fixed SINR target method:

The IoT distribution of γ = 0 is the minimum IoT value in the case where all MSs try to maintain the minimum transmission rate expected by the BS. The IoT value, an important measurement for intercell interference control, is jointly decided by SINR MIN (dB) and γ. The SINR (dB) determines the base value of IoT distribution, and γdetermines the IoT differential based on the base value. Fig. 7 shows IoT distribution for different SINR MIN values for γ = 0.2.

5.3. Comparison of Different Uplink Power Control Algorithms

In this section, we compare the performance of SMST with fractional power control (FPC) that was incorporated into 3GPP E-UTRA after Release8.

During the development of 3GPP LTE specifications, FPC was proposed [18]-[20] and used [17] as an OLPC method for uplink data channel physical uplink shared channel (PUSCH).

The key to FPC is to compensate the fraction of the path loss by control factorα, which can be expressed as PSD of each subcarrier, the same as in (22):

When α = 0 , the FPC algorithm degenerates to a fixed transmission PSD algorithm without affecting path loss. When α = 1, the FPC algorithm provides full path loss compensation and degenerates to the fixed target received signal strength (RSS) algorithm. The 3GPP specification [19] defines α from 0 to 1 as α∈｛0,0.4,0.5,0.6,0.7,0.8,0.9,1｝.The parameter, P0 , is also important in FPC algorithm. The P0 is mainly defined in two ways. In the first method of P0 selection,α is fixed as one selected optimum value, such as 0.8, in most published results, and P0 is searched for the optimum value in each simulation scenario. P0 is explicitly signaled by eNodeB [21],[22] with a large range.

For the scenario defined in Table 1, the results of SMST and FPC are shown on Fig. 8.

The performance trade-off of FPC is located in the range of P0 larger than -79 dBm. If the P0 is not well selected, for example, when P0 < -79 dBm, the sector SE and cell-edge SE degrades at the same time. Similar evaluation results can be found in [23] and [24], where the performance of sector throughput and cell-edge throughput are shown separately by IoT level. Here, the IoT level is directly controlled by P0.

When the selected optimum performance point of FPC is P0 = 79 dBm with fixed α = 0.8, the sector SE is 0.9375, and cell edge SE is 0.0447. Compared with the SMST algorithm results without optimum searching for SINR MIN ( the value is just set as 0 dB), there is still big performance gap. If SMST maintains the same sector SE as FPC optimum point of 0.9375, the SMST can provide cell-edge SE of 0.0687, which is a 53.69% gain over 0.0447 of FPC optimum cell-edge SE. If SMST maintains the same cell-edge SE as FPC optimum point of 0.0447, the SMST can provide sector SE of 1.2404, which is a 32.31% gain over the 0.9375 of FPC optimum-sector SE. The average performance gap between SMST and FPC is 43%. In the second method of P0 selection, P0 is transformed fromα value and cell-edge target SNR, as suggested in [23] and given by

where SNRTarget is the cell edge target SNR, PSDn is the thermal noise PSD, and PSD Max is the maximum transmission power PSD for assigned resource size.

Equation (26) provides the connection betweenαand P0 . As a result, if α = 0 , then (25) becomes

FPC degenerates to a maximum transmission power scheme. If α = 1, then (25) becomes

FPC degenerates to a fixed receiving-target SNR method. A comparison of the performances of fixed-target SNR is shown in Fig. 9.

In Fig. 9, the optimal performance point of FPC algorithm is difficult to identify. One selected performance point for FPC (SNRTarget = 6 dB ,α = 0.6) is used for performance comparison, its sector SE is 1.0799, and its cell-edge SE is 0.0350. If SMST maintains the same sector SE as FPC selected point of 1.0799, the SMST can provide cell-edge SE of 0.0607, which is a 73.43% gain over 0.0350 of FPC selected cell-edge SE. If SMST maintains the same cell-edge SE as FPC optimum point of 0.0350, the SMST can provide sector SE of 1.2904, which is 19.49% gain over 1.0799 of FPC selected sector SE. Also, the average gain of SMST compared with FPC can be as much as 46.46%. From Fig. 8 and Fig. 9, SMST performs 40% better than FPC.

**6 Conclusion and Discussion** In this paper, we have proposed a novel uplink power control algorithm, SMST, for MIMO-OFDMA systems. We also performed extensive system-level simulations to compare different uplink power control algorithms, including the FPC adopted in 3GPP LTE and LTE-Advanced. Our results show that SMST adopted in IEEE 802.16m outperforms other algorithms in terms of spectral efficiency, cell-edge performance, interference control, and tradeoff control between sector-accumulated throughput and cell-edge user throughput. The SMST performance gain over FPC can be more than 40%.

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**Biographies**

**Rongzhen Yang** (rongzhen.yang@intel.com) received his B.S. and M.S.degrees in electrical engineering from Shanghai Jiaotong University in 1997 and 2000. He was a software engineer at Intel's China Software Lab from 2000 to 2002, a researcher at Intel Research from 2003 to 2004, and a wireless security architect at Intel APAC Wireless Security from 2005 to 2006. He is currently a system engineer of advanced wireless technology at Intel Corporation. Rangzhen Yang’s research interests include technology development for advanced wireless standards in personal, local, and wide area wireless networks. He has written more than 10 journal and conference articles and has more than 40 patents.

**Hujun Yin** (hujin.yin@intel.com) received his B.S. and an M.S. degrees from Shanghai Jiaotong University in 1995 and 1998. He received his Ph.D. in electrical engineering from the University of Washington in 2001. From 2001 to 2002, he was a senior researcher at AT&T Research, where he focused on wireless network management and optimization research. From 2002 to 2004, he was a senior wireless architect at ViVATO, where he was responsible for smart antenna enhanced 802.11 WLAN network solutions. Dr. Yin is currently a principal engineer and director of advanced wireless technology at Intel Corporation. He leads technology development for advanced wireless standards in personal, local, and wide area wireless networks. Dr.Yin has more than 20 journal and conference articles and has over 50 patents.

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