# 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

$$\frac{C}{N_0} = \frac{P_t G_A G_B}{d^{\alpha}N_0},$$

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.

$$\gamma_0 \propto \Big( \frac{P_t}{R_b} \Big).$$

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

$$E_t \propto P_t\frac{L}{R_b}=\gamma_0 N_0 L,$$

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

## 2 Answers

Note that there are a host of practical secondary effects of increasing transmission power that do not scale with potentially less required transmission time, such as: battery impedance, voltage converter startup time, oscillator stabilization and carrier synchronization time, leakage or resistive losses due to larger required transistor sizes and/or higher voltage capacitors, more EMI shielding due to any higher digital edge rates required for processing, antenna shielding/spacing to limit human RF exposure, larger required heat spreaders/sinks, and etc. The goal is often to minimize, not transmission power, but all these secondary power losses or inefficiencies, and/or their associated device costs, assuming some lower bandwidth or latency of delivering messages meets design goal targets.

• This is very helpful, you are pointing out issues that I have not considered. But in fact, I thought there was a more fundamental reason for low-power oriented design (more linked to information theoretical aspects) but there actually isn't. I'm still doing some research on it and I'll try to complement your answer soon. – vaz Dec 10 '15 at 10:43
• Leaving aside regulatory constraints, I think this is the bulk of your answer. Everything is harder, more expensive, and less efficient at higher powers and faster speeds. As pointed out in the question, Eb is the driving factor and it doesn't care whether it uses more power or more time to achieve that goal. – Omegaman Jan 9 '16 at 2:51

After some research, I have found a paper that resumes well the answer to my question. As other people might be interested, here is a short summary:

Two important things to note: from a purely information theoretical approach, where only transmission power consumption is considered, it has been found that transmitting at infinite rate or at infinitely small rate maximises the bits-per-Joule capacity. By contrast, when circuit power is also considered---and of course, depending on the physical layer implementation---the overall energy-per-bit required for transmission may show different behaviours that depend on parameters such as communication distance (short/long range), duty-cycle, average message length, modulation and so no. The paper shows an example where the energy-per-bit required as a function of the rate shows an optimum minimum which is not at minimum rate, as information theory suggests.

• Many low power radio systems are using data rates significantly higher than required for the application and transmit in short bursts and sleep the remaining time. Very high data rates on other hand would require complex circuits or transmitting at higher frequencies with higher attenuation. Also look at the properties of digital logic: Lower clock frequencies are usually more energy effective, if you can still lower the operating voltage, but at some point you cannot scale down the voltage anymore and it becomes more effective to process in bursts and sleep and power gate to reduce leakage. – Jan Lucas May 27 '16 at 12:10