# Energy-Efficient Hardware Implementation of an LR-Aided K-Best MIMO Decoder for 5G Networks
## 5 Evaluation of Energy Costs of MIMO Detectors  
To design a green communication wireless system, it is important to reduce its overall power costs. Therefore, in order to analyse the energy efficiency of a MIMO decoding scheme in relation to a green wireless communication application, it is vital to consider both: the power consumption of the MIMO decoder hardware (\(P_{thr}\)) and also the minimum transmission power required for the decoder to work reliably (\(P_{tr}\)). Details on how each of these components can be evaluated are provided in the following two subsections:  
Power Consumption Estimation of MIMO Decoder  
The power dissipation of a hardware block (\(P_{hw}\)) is typically estimated as the sum of two components: dynamic and static. Dynamic power consumption (\(P_{dynamic}\)) is attributed to the charging and discharging of capacitances, it is dependent on the supply voltage (V), the operating frequency (f), the signals' transition activities (8), and the switching capacitances (C). Some of these factors are dependent on underlying CMOS technology used for implementation such as V, C, and f, whereas  
Figure 4: Hardware architecture of lr-aided k-best.  
others depend on the application running on the hardware such as (8). Dynamic power consumption can be computed as follows:  
\[P_{dynamic}=\delta.f.C.V^{2}. \tag{8}\]  
Static power consumption (\(P_{static}\)) is attributed to power dissipation caused by leakage currents and to short-circuit dissipation caused by current passing through the direct path between supply and ground during logical transitions in CMOS devices. Static power consumption is mainly a function of the implementation technology which determines the leakage currents and the supply voltage. The complexity of the circuit can affect static power dissipation, the more complex and the larger the design, the higher the amount of leakage power dissipation.  
In this work, to estimate the power consumption we have implemented the proposed decoder using 32 nm standard CMOS technology, with a supply voltage of \(1v\). The operation frequency was set to 253 MHz. More details on this is provided in Section 6.  
Estimation of Minimum Transmission Power RequirementA MIMO decoder typically has a required minimum SNR below which it cannot operate reliably. This essentially means there is a minimum required transmission power which can be calculated using the formulae below [19]:  
\[P_{tr}=10^{\frac{RNF}{10}}\;kTB\;\left(\frac{S}{N}\right)\left(\frac{4\pi}{ \lambda}\right)^{2}\;d^{n} \tag{9}\]  
where:  
\begin{tabular}{l l} \(\text{S/N:}\) & is the minimum signal to noise ratio required at the receiver. \\ \(\text{RNF:}\) & is a the receiver noise figure in dB, (e.g., for an ideal receiver (RNF = 0). \\ \(\text{K:}\) & is the Boltzmann constant. \\ \(\text{T:}\) & is the absolute temperature in K. \\ \(\lambda\) & is the transmitted wavelength. \\ \(d\) & is the distance between the transmitter and receiver \\ \(n\) & is the path loss exponent which depends on the environment (e.g., for free space (\(n=2\))). \\ \end{tabular}  
In this work, Equation (9) is used to estimate the minimum requirement for transmission power of MIMO detection schemes