Hirley Alves - Wireless RF Energy Transfer in the Massive IoT Era: Towards Sustainable Zero-energy Networks (IEEE Press)

Traditional communication systems are often designed and optimized using the notion of channel capacity, which is a reasonable benchmark for systems using long block transmissions. However, many IoT applications and mMTC are often characterized by short packets, periodic data traffic, and above all, by a massive number of deployed devices. As a result, the same assumptions in terms of channel capacity cannot be directly applied to short block length messages [289]. In this context, new theoreticcal results related to the performance of short block length communication systems have shown that the achievable rate depends not only on the channel quality of the communication link, but that it is also a function of the actual block length and error probability tolerable at the receiver [75, 289, 290].

In light of these new results, the underlying channel models need to be revisited for IoT specific environments. Therefore, it is possible to design new protocols that account for such short messages and then optimize coding strategies, as well as rate adaptation and power allocation policies, e.g., as in [76, 77, 164, 165, 237, 291293]. The literature is growing since Poliyanskys seminal paper [75]. The surveys in [289, 290] provide an account of the key findings in the recent years. All in all, these results are fundamental to understanding the trade-offs between message payload and size (block length), and, therefore, reliability, latency, and data rate.

Assume a source wants to communicate with a destination. The source, an MTD or IoT device, conveys a message composed of a payload of b bits. This message is overall short, i.e., spans over a limited number n of channel uses, and, therefore, requires analysis with a new set of information-theoretical tools [75, 289, 290].

The encoder maps the sequence of b information bits to a sequence of information symbols of length n, which are then transmitted over the wireless channel. Then, the decoders job is to guess the information bits that were transmitted. When the decoder guesses incorrectly, an error is declared. Mathematically, the encoding and decoding translates as follows.

The source transmits its message {1,,L} using a (n,L,P,) code, where n is the block length, L is the codebook size, P is the power constraint, and is the maximum error probability constraint. Thus, the (n,L,P,) code comprises:

• An encoder :{1,,L}Cn, which maps the message into a length-n codeword x{x1,,xL} satisfying the power constraint
  (A.1)

  Observe that in the context of , the available power P is a function of the harvested energy.

• A decoder :Cn{1,,L} satisfying the maximum error probability constraint
  (A.2)

  where y denotes the channel output induced by the transmitted codeword at the end of each transmission.

Notice that the rate r is defined as the fraction bn of information bits to the number of transmitted symbols. Ideally, we attempt to design the code such that r is as large as possible, while the error probability is as small as possible. Bearing this in mind, we can define the maximum channel coding rate r*(n,L,P,) as the largest rate log2Ln (measured in bits per channel use bpcu) for which there exists a code (n,L,P,), which mathematically translates to

(A.3)

Then, P, b, n and are related according to (A.). Polyanskiy et al. [75] provide an accurate characterization of the trade-off between these parameters in AWGN channels as follows

(A.4)

where (a) is a Gaussian approximation introduced in [75] that holds tight for n100 channel uses. Herein,

(A.5)

is the Shannon capacity, and

(A.6)

is the channel dispersion, which measures the stochastic variability of the channel relative to a deterministic channel with the same capacity. In addition, Q1() denotes the inverse Q-function.

Figure A.) assuming an AWGN channel with SNR of 10 dB. Notice that as the block length grows, n, the achievable rate r approaches the Shannon capacity as expected. Also notice that for small block length, for instance n < 1000, there is a large performance gap between finite and infinite case, and this gap grows larger as increases.

Rate r as function of the block length n for different values of error probability and = 10 dB.

Now, we can rewrite (A.) as

(A.7)

which is the maximum error probability when transmitting b information bits over a channel with SNR and using n complex symbols. Notice that (A.) matches the asymptotic outage probability when n and/or 0. Meanwhile, for block fading channels, the average maximum error probability is [292]

(A.8)

since the channel becomes conditionally Gaussian on , and we only require to take expectation over the SNR to attain the corresponding average error probability. However, the effect of the fading on (A.), is a good match in such cases and is given by

(A.9)

The behavior of (A., which shows the average maximum error probability, (b,n), (often called outage probability) as function of the block length n. Note that increases in the block length n or increases in the SNR lead to a decrease in the outage probability. However, increases in the message payload b worsen the outage probability because they induce a higher rate since r=bn.

Average maximum error probability as function of the block length