A semi-static power control and link adaptation method is proposed in this section to improve the EE while guaranteeing the MCS level constraint. Different from the previous energy efficient schemes which are only applicable for the Shannon capacity, our proposed scheme determines the energy efficient transmit power and MCS level according to a practical EE estimation mechanism, which is based on CQI feedback. Furthermore, we propose a semi-static dual trigger to control the transmit power and MCS level configuration, which is practical in the HSDPA systems.

Figure 3 shows the operational flowchart of the proposed power control and link adaptation procedure at the Node B. As long as CQI and acknowledgement/negative acknowledgement(ACK/NACK) information are received by the Node B, Node B can estimate the EE and the required transmit power for each MCS level based on the estimation mechanism. Then Node B can determine the MCS level and transmit power with maximum EE. After that, the Node B will determine whether they need to be configured immediately or not, where a semi-static dual trigger mechanism is employed. If it is triggered, the derived optimal transmit power and corresponding optimal MCS level will be reconfigured. In this way, the scheme is realized in a semi-static manner. There are two benefits here. For one thing, the semi-static feature makes the scheme practical in HSDPA which does not support inner loop power control. For another, the cost of signaling can be reduced significantly through controlling the power reconfiguration cycle length adaptively.

In the following subsections, we will introduce the scheme in details.

### 3.1 EE estimation and optimal transmit power determination

We propose the addition of an EE estimation mechanism to the traditional link adaptation operation, whereby it employs the MCS table to estimate the EE and required transmit power for different MCS levels based on CQI feedbacks, and then determines the EE optimal transmit power and MCS level. The MCS table here is defined as the mapping relationship between HS-PDSCH received signal to interference and noise ratio (SINR) threshold and the corresponding feedback CQI index, based on the initial BER target *Γ*_{tar}. Each CQI index corresponds to a dedicated MCS level in HSDPA. An example of TABLE G [3] is shown in Figure 4.

At first, we need to estimate the transmit power required for different MCS levels. According to [13], the SINR of HS-PDSCH is denoted as

\rho \left({P}_{HS}\right)=\frac{SF\cdot {P}_{HS}g}{\left(1-\alpha \right){I}_{\text{or}}+{I}_{\text{oc}}+{N}_{0}W},

(7)

where *SF*, *P*_{
HS
}, *g*, *α*, *I*_{or}, and *I*_{oc} denote the spreading factor, HS-PDSCH power, the instantaneous path gain, the channel orthogonality factor, the total received power from the serving cell and the inter-cell interference, respectively. As the link level simulation has captured the effect of the inter-code interference, according to (7), received SINR is proportional to transmit power *P*_{
HS
} assuming that the interference is constant. By taking the logarithm on both sides of (7), we can find that the difference between two transmit power *P*_{1} and *P*_{2} is equal to the difference between the two SINR *ρ*(*P*_{1}) and *ρ*(*P*_{2}) derived from them:

{P}_{1}\left(\text{dBm}\right)-{\text{P}}_{2}\left(\text{dBm}\right)=\rho \left({\text{P}}_{1}\right)\left(\text{dB}\right)-\rho \left({\text{P}}_{2}\right)\left(\text{dB}\right),

(8)

where transmit power is measured in dBm and SINR is measured in dB.

After replacing the actual SINRs in (8) By the SINR thresholds in the MCS table, we can utilize the equation to estimate the transmit power required for the MCS levels. In other words, we propose to approximate the difference between the transmit power required for two MCS levels as the difference between the two's SINR thresholds. For example, assume that the current transmit power is *P* and the feedback CQI index is *i*. For an arbitrary CQI index denoted by *j*, the corresponding SINR threshold is denoted as *β*_{
j
} and the MCS level denoted as *θ*_{
j
}. We can estimate the transmit power *P*_{
j
} required for MCS level *θ*_{
j
} as follows:

{P}_{j}=P+{\beta}_{j}-{\beta}_{i}+\delta .

(9)

The offset *δ* here is to deal with the impact of channel variations which can be determined based on the feedback ACK/NACK information from the user side.

In the simplest case, *δ* can be set to zero and (9) can be rewritten as:

{P}_{j}=P+{\beta}_{j}-{\beta}_{i}.

(10)

Note that transmit power is measured in dBm and SINR threshold is measured in dB in (9) and (10).

One may argue that the adjustment would cause the variation of BER, and then affect the average number of the retransmissions, which may cause the energy wasting. This is not the case. The same BER can be guaranteed for the current and adjusted power level and MCS level, which can be explained as follows. Note that the MCS table at both the BS and the user is based on a fixed BER target. Therefore, it is obvious that the current power level and feedback CQI can guarantee the BER. During the adjustment, to make sure the same BER can be guaranteed, the transmit power and the MCS level are jointly adjusted. That is to say, when the transmit power is decreased, the corresponding MCS level should also be decreased. As the same BER is guaranteed in this way, the same retransmission probability can also be guaranteed, and the average number of the retransmissions will not be affected. In a word, our scheme would work well without affecting the mechanism of the retransmission, which is practical in real systems.

Then the estimation of EE for the MCS level *θ*_{
j
} is given by:

{\xi}_{j}=\frac{{\tau}_{j}}{{t}_{\text{s}}\cdot \left(\frac{{p}_{j}}{\eta}+{P}_{\text{Dyn}}+{P}_{\text{Sta}}\right)},

(11)

where *τ*_{
j
} represents the transport block size of the MCS level *θ*_{
j
} , and *t*_{s} is equal to two milliseconds and represents the duration of one TTI for HSDPA. Then we compare the estimated EE for each MCS level, determine the optimal CQI index *j** by

{j}^{*}=\underset{j}{\text{arg}\phantom{\rule{2pt}{0ex}}\text{max}}{\xi}_{j}.

(12)

The corresponding MCS level is denoted as *θ*_{j*}and the required transmit power denoted as {P}_{{j}^{*}}.

As the minimum MCS level of the user is *θ*_{min} and the maximum transmit power of the Node B is *P*_{max}, the constrained optimal MCS level and the optimal transmit power can be given by:

\begin{array}{cc}\hfill {\theta}_{\text{opt}}& =\text{min}\left(\text{max}\left({\theta}_{\text{min}},\phantom{\rule{2.77695pt}{0ex}}{\theta}_{j*}\right),\phantom{\rule{2.77695pt}{0ex}}{\theta}_{\text{max}}\right),\hfill \\ \hfill {P}_{\text{opt}}& =\text{min}\left(\text{max}\left({P}_{\text{min}},\phantom{\rule{2.77695pt}{0ex}}{P}_{j*}\right),\phantom{\rule{2.77695pt}{0ex}}{P}_{\text{max}}\right).\hfill \end{array}

(13)

The same estimation mechanism above can be employed to determine the corresponding minimum transmit power *P*_{min} and the corresponding maximum MCS level *θ*_{max}. Correspondingly, the estimated EE for the optimal MCS level and transmit power is denoted as *ξ*_{opt}.

In our proposed algorithm, only the feedback CQI and ACK/NACK information are necessary for Node B to do the EE estimation and energy efficient power determination.

### 3.2 Semi-static power reconfiguration trigger

However, the power configuration cannot be performed instantaneously due to the following two reasons. For one thing, the support for fast AMC and HARQ functionality in HSDPA does not allow the transmit power change frequently. For another, in order to guarantee the accuracy of the CQI measurement and user demodulation especially for high order modulation, Node B should inform the user of the transmit power modifications through the signalling called measurement power o set (MPO) in radio resource control (RRC) layer when the transmit power is reconfigured. If the configuration performs frequently, the signaling overhead is significant. Therefore, we propose a semi-static trigger mechanism to control the procedure.

Assume that the EE derived from the last transmission is *ξ* , define relative EE difference *D* as follows:

D=\frac{{\xi}_{\text{opt}}-\xi}{{\xi}_{\text{opt}}}.

(14)

In our proposed scheme, the minimum trigger interval is set to be *γ*_{prohibit}, and the maximum trigger interval to be *γ*_{periodic} which satisfies *γ*_{periodic} ≫ *γ*_{prohibit}. A timer is used to count the time from the last power configuration and the timing is denoted as *t*.

First, if

\left\{\begin{array}{c}D\ge \Delta \hfill \\ t>{\gamma}_{\text{prohibit}}\end{array}\right.

(15)

both are satisfied, the proposed energy efficient power configuration and corresponding MCS reselection process is triggered. This event trigger can guarantee EE gain and also avoid frequent power configuration. On the other hand, if

t>{\gamma}_{\text{periodic}}

(16)

is satisfied, the power configuration process must be triggered regardless of the value of *D*. This periodical trigger ensures that the scheme is always active and gurantees the EE gain. If the power configuration is triggered, the timer must be reset to zero. The whole trigger mechanism above is robust as its parameters can be configured adaptively according to actual systems. It can be implemented practically in HSDPA and signaling overhead can be reduced.