# What are the fundamental reasons that suggest us to minimise transmission power for energy-efficient radio link design?

My question in short:

Under which scenarios minimising transmission power is beneficial in terms of transmitter energy-efficiency? is there any fundamental reason to keep a low-power oriented design strategy?

In particular, small, low-cost transceivers (such as those used for M2M/IoT communications) are designed according to this strategy. I'd like to understand why.

Background

It is quite natural to think that energy efficiency in radio link design is directly linked to a low transmission power. This, however, cannot be concluded from a simple analysis (see baseline model below). For instance, we may feel tempted to decrease the data rate in order to reduce the required transmission power. This in turn increases the transmission time, and the total energy consumed does not change.

Naturally, this question requires a look to the whole transmitter circuitry (which is a little outside my field). After some research, I noted that there must be a trade off regarding clock rate (high-precision and high-rate is payed with extra power) and amplifier efficiency (lower input powers are usually less efficient). But this suggests that minimising power is not always the best option.

The baseline model (optional)

Consider a wireless radio system where a transmitter $A$ wants to communicate with a receiver $B$, at distance $d$. The total attenuation (due to to signal propagation) can be simply modelled as $L=d^\alpha$, where typically $2 \leq \alpha \leq 4$.

The carrier-to-noise density ratio $\frac{C}{N_0}$ at $B$'s receiver input is

\begin{equation} \frac{C}{N_0} = \frac{P_t G_A G_B}{d^{\alpha}N_0}, \end{equation}

where $P_t$ is the power at the output of $A$. When designing these systems, there is usually a performance constraint expressed as a maximum tolerated bit error rate, which turns into a minimum $E_b/N_0 = \gamma_0$ requirement.

So in order to achieve this $\gamma_0$, it seems that there are only two system design parameters to play with (assuming all other parameters are fixed): transmission power and data rate, i.e.

\begin{equation} \gamma_0 \propto \Big( \frac{P_t}{R_b} \Big). \end{equation}

Thus, we observe that increasing the transmission power has the same effect that decreasing the data rate, in terms of $E_b/N_0$.

Now consider that the total amount of data to be delivered is $L_b$. The total energy consumed by $A$ to deliver $L_b$ bits is therefore

\begin{equation} E_t \propto P_t\frac{L}{R_b}=\gamma_0 N_0 L, \end{equation}

which does not depend on the operating power neither on the data rate.

• Can you please clarify what your question is? Also: many of the variables in a communication system (power, energy, rate, bandwidth, SNR, BER, etc) are inter-related; your analysis looks correct to me. The key problem is to select values for each variable so that you meet your design requirements. – MBaz Dec 9 '15 at 14:37
• Edited. Do you think it's clear enough now? – vaz Dec 9 '15 at 15:10
• I think it's clearer now, thanks. You'll probably be interested in this paper: ieeexplore.ieee.org/xpl/… – MBaz Dec 9 '15 at 16:32
• Nice paper @MBaz, thanks. Though I've already read similar papers regarding 5G networks and generic ad-hoc networks, and they are often devoted to energy efficiency optimisation at the network level (and thus not at terminal's physical layer level). – vaz Dec 9 '15 at 16:51
• One thing I take away from those papers is that you need to apply Amdahl's law: in some cases, power at the terminal is not what should be optimized, at least not at first. Having said that, at the terminal you want: long battery life, high bit rate, low error rate, and efficient bandwidth use. Since those are mutually exclusive, you need to select and then maximize some metric. Note that some systems, like deep-space probes, which are power-limited, do transmit very slowly in order to achieve good BER. – MBaz Dec 9 '15 at 18:15