**4. Experimental study of AFCS functioning**

**3.3 Adaptive auto-adjusting AFCS to the scenario of application**

transmission <sup>δ</sup> <sup>¼</sup> ffiffiffiffiffi

δ*<sup>L</sup>* is a variable parameter.

with known variance *σ*<sup>2</sup>

estimates *x*^ð Þ<sup>1</sup>

MSE value *<sup>L</sup>*^*opt*

and estimates *x*^ð Þ<sup>1</sup>

sequence of signals *y*

sequence *x*^ð Þ<sup>1</sup>

together with *P*min

cycle of AFCS adjusting:

*<sup>L</sup>*^*opt* <sup>1</sup> , *<sup>P</sup>*^min

*<sup>x</sup>* � *<sup>x</sup>*^ð Þ *<sup>m</sup>*

**Figure 3.**

**16**

*under fixed optimal gains* M*opt*

*Pk*

*Modulation in Electronics and Telecommunications*

0. In the first cycle, the modulation index *Mopt*

> <sup>1</sup> , … , *<sup>x</sup>*^ð Þ *<sup>M</sup>* 1 � �

> > ð Þ *m*

adjusted AFCS begins nominal functioning.

<sup>1</sup> *.*

<sup>1</sup> , … , *<sup>x</sup>*^ð Þ *<sup>M</sup>* 1 � �

<sup>2</sup> <sup>¼</sup> *<sup>A</sup>*0*Mopt*

estimates, environmental characteristics, and other factors.

<sup>2</sup> *e* ð Þ *m*

sequence in the same way as in first cycle. The computed values *P*min

*Mk* set to the values (27) and gain *L*<sup>∗</sup>

<sup>1</sup> , … , *<sup>x</sup>*^ð Þ *<sup>M</sup>* 1 � �

The adjusting algorithm uses the "resonance" effect that is increase of MSE, if the values of parameters *Lk*, *Mk* decline from their optimal values (16), (27). The effect is illustrated in **Figure 3** which shows the changes of relative errors of

To adjust the parameters, the system utilizes two identical testing sequences of Gaussian samples *x*ð Þ<sup>1</sup> , … , *x*ð Þ *<sup>M</sup>* � � whose codes are stored in the memory of the BSt processor and the FT microcontroller (or BSt transmits these sequences to FT over feedback). All the samples in the testing sequence are zero mean Gaussian values

the FT sends to the BSt the written testing sequence of samples *x*ð Þ<sup>1</sup> , … , *x*ð Þ *<sup>M</sup>* � �, the same one that is stored in the processor of BSt. The BSt processor computes the

<sup>1</sup> , and *<sup>x</sup>*ð Þ<sup>1</sup> , … , *<sup>x</sup>*ð Þ *<sup>M</sup>* � � are stored. Simultaneously, the BSt sends values *<sup>P</sup>*min

In this cycle, the microcontroller of the FT forms the sequence of signals *e*

and sets the gain of AM modulator to this value. So adjusted, the FT transmits the

next cycle of adjusting realized according to the same scheme as in the previous cycle. The subsequent cycles repeat these operations. After the M-th cycle, the

is replaced by the new sequence *x*^ð Þ<sup>1</sup>

The duration and frequency of adjustments depend on the dynamics of scenario changes, processors' rate, channel bandwidth, requirements for the accuracy of

*Changes of mean relative error of estimates depending on the deviation of the gains* Lk *from optimal values* L*opt*

<sup>2</sup> is transmitted to the FT. The receipt of these values initializes the

<sup>1</sup> , (*<sup>m</sup>* <sup>¼</sup> 1, … , M), computes the optimal value of the gain *<sup>M</sup>opt*

<sup>1</sup> and computes the corresponding value *<sup>P</sup>*^min

<sup>p</sup> *<sup>=</sup>σ*<sup>0</sup> (normalized root mean square error—RMS) under gains

and values of MSE *P*1. It also searches for the minimizing

to the FT. Reception of these data initiates the second

<sup>2</sup> to the BSt, which processes the received

*<sup>k</sup>* ¼ *Lk*ð Þ 1 þ δ*<sup>L</sup>* , where *Lk* has the value (16) and

<sup>1</sup> is set to the known value 1*=α*σ0, and

<sup>1</sup> . The computed values

<sup>2</sup> ¼ 1*=α*

<sup>2</sup> , *<sup>L</sup>opt*

<sup>2</sup> , … , *<sup>x</sup>*^ð Þ *<sup>M</sup>* 2 � � 1

ð Þ *m* <sup>2</sup> ¼

<sup>2</sup> are stored,

, and

ffiffiffiffiffiffiffiffiffi *P*min 1 q

,

k

The prototype of AFCS was designed on the basis of the optimal transmissionreception algorithm(6)–(8), using and parameters set to the values (16), (18), (or in **Table 1**, for *σ*<sup>2</sup> *<sup>v</sup>* ¼ 0), and general principles of AFCS transmission described in Section 3.1. The layouts of the transmitting (FT) and receiving (BSt) modules are shown in **Figure 4a**, **b**.

The transmitter was realized using narrowband adaptive AM modulator followed by the programmable voltage-controlled oscillator VG7050EAN (power 10 dBm, carrier frequency 433.2 MHz). The feedback channel was realized using digital receiver RFM31B-S2 and transmitter RFM23B (power 27 dBm, carrier frequency 868.3 MHz). This ensured virtually ideal feedback transmission of signals in the indoor and outdoor experiments carried out at distances to 100 meters (straight line view, FT with ceramic mini-antennas, BSt with quarter-wave antennas).

At the beginning of every new series of experiments, a self-adjusting algorithm was activated, which set the parameters *Mk* and *Lk* to the values optimal for the given scenario.

The main measured characteristic of the prototype was the *dependence of* MSEn½ � dB *on the number of transmission cycles. The experiments were* carried out at different distances between the FT and BSt. Typical dependencies of MSEn½ � dB on *n* at the distances of 40, 50, and 75 meters are shown in **Figure 5**.

The plots are presented in the decibel scale, and the nearly linear dependence of the measured values MSEn½ � dB on the number of cycles means that, on a linear scale, MSE decreases exponentially. According to the results of Section 3.2 (formula (19)), this is possible, if the system transmits signals perfectly, with a bit rate *equal to the capacity* of the system. In this case, spectral and energy efficiencies of transmission also attain the limit values.

Moreover, plots in **Figure 5** allow for a sufficiently accurate evaluation of the characteristics of the system. With this aim, let us rewrite the expression of spectral efficiency (33) in the decibel scale in the form (the confirmed close to perfect transmission permits us to write that *R* ¼ *C*):

$$\frac{C\_n}{F\_0} = \frac{3.32}{n} \log\_{10} \frac{\sigma\_0^2}{P\_n} = -\frac{0.332}{n} \text{MSE}\_n[\text{dB}].\tag{39}$$

**Figure 4.**

*Layout of PCB modules of prototype of perfect AFCS: (a) forward transmitter integrated with sensor; (b) base station.*

#### **Figure 5.**

*Values* MSEk½ �¼ dB f kð Þ *measured at the distances of 40, 50, and 75 meters (indoor experiments).*


#### **Table 2.**

*Measured characteristics of the prototype.*

The linear approximation of the plots in **Figure 5** in first *n* ¼ 10 cycles allows for evaluation of the ratio MSE*n*½ � dB *=n* directly from the plots. Substitution of these values into (39) gives the numerical estimates of the spectral efficiency for each distance. In turn, perfect mode of transmission allows for the evaluation of the power efficiency using formula (3) and measured values of the spectral efficiency *Cn=F*0. The obtained results are presented in **Table 2** and illustrated on the energyspectral plane in **Figure 6**.

conditions is to be continued. It is worth noting that the utilization of the quarterwave antennas provided sufficiently stable sample transmission at distances upto

*Dependencies* MSEk½ �¼ dB f kð Þ *measured with the intervals in 2–3 minutes at the distance of 50 m (indoor experiments): (a) power of FT transmitter 10 mW, ceramic mini-antennas; (b) power of FT transmitter*

*Two-dimensional plot presenting values (red points) of the energy-spectral efficiency of optimal AFCS*

*Perfect Signal Transmission Using Adaptive Modulation and Feedback*

*DOI: http://dx.doi.org/10.5772/intechopen.90516*

The experiments confirmed the feasibility of the perfect AFCS, as well as the capability of modulation and feedback to ensure the perfect signal transmission.

The chapter gives a brief outlook of the approaches to design of the currently not used class of communication systems which may substantially improve the efficiency and performance of the wireless low-power transmission. The presented results develop excellent but not finished and today almost forgotten research in FCS theory carried out in the years 1960–1970. These investigations were first steps toward the formation of the second direction in information theory: the theory of the systems with feedback channels. However, in the middle of 70s, the research

80–90 m using FT with the power reduced to 1 mW.

**5. Discussion of results**

*1 mW, quarter-wave antennas.*

was hampered.

**19**

**Figure 7.**

**Figure 6.**

*measured at the distances in 40, 50, 75 meters.*

The plots in **Figure 7a**, **b** illustrate the results of measurements carried out at the fixed distance sequentially, with the time interval in 1–3 minutes.

All the experiments confirmed the existence of the initial interval 1≤*k*≤*n*<sup>∗</sup> of the perfect transmission, as well as the efficiency of the developed algorithm of AFCS auto-adjusting. On average, at the distances of 40–50 m, the accuracy of transmission attained the values of 10�<sup>4</sup> order in 5÷7 cycles of the sample transmission. In several experiments, accuracy attained the order of 10�<sup>7</sup> ÷ 10�<sup>10</sup> and greater, but the results were non-stable (see, e.g., plots in **Figure 7a**, **b**).

It was also noted the growing influence of the external disturbances and noises on the further changes of MSE if it attained sufficiently small values. Since this time, MSE decreased with the growing fluctuations, sometimes regularly but at the smaller rate. This could not be an effect caused by saturations: experiments were carried out under saturation factor *α* ¼ 3 that reduced the cases of saturations to 0.5–1 percent of the transmitted samples. A study of the AFCS functioning in real

*Perfect Signal Transmission Using Adaptive Modulation and Feedback DOI: http://dx.doi.org/10.5772/intechopen.90516*

#### **Figure 6.**

*Two-dimensional plot presenting values (red points) of the energy-spectral efficiency of optimal AFCS measured at the distances in 40, 50, 75 meters.*

#### **Figure 7.**

The linear approximation of the plots in **Figure 5** in first *n* ¼ 10 cycles allows for evaluation of the ratio MSE*n*½ � dB *=n* directly from the plots. Substitution of these values into (39) gives the numerical estimates of the spectral efficiency for each distance. In turn, perfect mode of transmission allows for the evaluation of the power efficiency using formula (3) and measured values of the spectral efficiency *Cn=F*0. The obtained results are presented in **Table 2** and illustrated on the energy-

*Values* MSEk½ �¼ dB f kð Þ *measured at the distances of 40, 50, and 75 meters (indoor experiments).*

Distance (m) 40 50 75 MSE*n* [dB]/*n* �6.25 �4.4 �1.4 *Csyst=F*<sup>0</sup> 2.07 1.46 0.465 *Q2* 3.21 1.75 0.375

*<sup>n</sup> =N<sup>ξ</sup>* 1.76 1.19 0.8

*<sup>n</sup> =N<sup>ξ</sup>* [dB] 1.85 0.76 �0.92

The plots in **Figure 7a**, **b** illustrate the results of measurements carried out at the

All the experiments confirmed the existence of the initial interval 1≤*k*≤*n*<sup>∗</sup> of the perfect transmission, as well as the efficiency of the developed algorithm of AFCS auto-adjusting. On average, at the distances of 40–50 m, the accuracy of transmission attained the values of 10�<sup>4</sup> order in 5÷7 cycles of the sample transmis-

It was also noted the growing influence of the external disturbances and noises on the further changes of MSE if it attained sufficiently small values. Since this time, MSE decreased with the growing fluctuations, sometimes regularly but at the smaller rate. This could not be an effect caused by saturations: experiments were carried out under saturation factor *α* ¼ 3 that reduced the cases of saturations to 0.5–1 percent of the transmitted samples. A study of the AFCS functioning in real

÷ 10�<sup>10</sup> and

fixed distance sequentially, with the time interval in 1–3 minutes.

sion. In several experiments, accuracy attained the order of 10�<sup>7</sup>

greater, but the results were non-stable (see, e.g., plots in **Figure 7a**, **b**).

spectral plane in **Figure 6**.

*Measured characteristics of the prototype.*

*Modulation in Electronics and Telecommunications*

**Figure 5.**

*Ebit syst*

*Ebit syst*

**Table 2.**

**18**

*Dependencies* MSEk½ �¼ dB f kð Þ *measured with the intervals in 2–3 minutes at the distance of 50 m (indoor experiments): (a) power of FT transmitter 10 mW, ceramic mini-antennas; (b) power of FT transmitter 1 mW, quarter-wave antennas.*

conditions is to be continued. It is worth noting that the utilization of the quarterwave antennas provided sufficiently stable sample transmission at distances upto 80–90 m using FT with the power reduced to 1 mW.

The experiments confirmed the feasibility of the perfect AFCS, as well as the capability of modulation and feedback to ensure the perfect signal transmission.

#### **5. Discussion of results**

The chapter gives a brief outlook of the approaches to design of the currently not used class of communication systems which may substantially improve the efficiency and performance of the wireless low-power transmission. The presented results develop excellent but not finished and today almost forgotten research in FCS theory carried out in the years 1960–1970. These investigations were first steps toward the formation of the second direction in information theory: the theory of the systems with feedback channels. However, in the middle of 70s, the research was hampered.

The main reason for the difficulties was the lack of practical results. Another, less obvious source of failures was the omission of possible saturation of modulators or emitters in the forward transmitters. The not less crucial obstacle also was not discussed in the literature which is the dependence of the CS performance on the scenarios of application.

Moreover, the signals generated by the transmitters of CSC are discrete, their form is fixed and in no way depends on the input signals. Information is delivered by combinations of the symbols of code. There is no possibility to regulate the quality of the transmission aside from the external regulation of the power of transmitter or switching the codes. Meanwhile, the quality of transmission provided by the adjusted perfect AFCS depends on the scenario of their application, but

General evaluation of the future perspectives of AFCS: currently, almost all CS and networks have feedback channels, and AFCS could solve many of the aforementioned and other problems. Below, we attach a summary of possibilities of the perfect AFCS, which have been established and verified in [36–41] and other works.

1.Perfect AFCSs provide the most energy-spectral efficient transmission of signals in real time with the limit energy-spectral efficiency, bit rate equal to the capacity of forward channel, and minimal MSE of the signals reception.

2.The absence of coders allows for the construction of a full mathematical model of transmission, from the source of signals to the BSt processor. This model enables the formulation of a clear analytical criterion (MSE), the application of Bayesian estimation theory, and the derivation of optimal transmission-reception algorithms determining the approach to the perfect

3.Feedback channel and optimal transmission algorithms enable the

4.The side effect of AFCS adjustment is that the BSt computes the on-line estimates of MSE, SNR, and capacity of the system. These data permit to evaluate the current energy-spectral efficiency of transmission and to

required accuracy of the signal recovered.

energy efficiency of transmission.

development of adaptive algorithms adjusting the parameters of AFCS to the environment changes. This permits the system to maintain the perfect mode of transmission in different, also non-stationary scenarios. De facto, the system regulates its own capacity, adjusting it to the changes of environment.

decrease the losses of energy regulating the number of cycles maintaining the

5.The analytical expression for MSE of transmission has an empirical analog, whose values can be measured and used for evaluation of the performance of every CS used for the analog signals transmission. As shown in Section 3, MSE permits us to determine the quality of transmission, bit rate, as well spectral efficiency of every CS. For the perfect AFCS, minimal MSE determines the

6. Signals emitted by the FT have the form of realizations of the (stationary) pulse white Gaussian noise. The amplitudes of each emitted pulse depend on random values of the signals *ek* at the input of the modulator, and values of the adjusted parameters *Mk* depend on the scenario, which excludes data interception and ensures secure forward transmission. The full protection of the system depends on protecting the feedback channel and can be provided

7.The absence of coding units simplifies the architecture of the FT, as well as reduces their energy consumption, complexity, and cost, which allow for the

by applying well-protected codes and directed antennas.

development of efficient battery-less AFCS.

**21**

always attains the limit or close to the limit values.

*DOI: http://dx.doi.org/10.5772/intechopen.90516*

*Perfect Signal Transmission Using Adaptive Modulation and Feedback*

AFCS design.

The chapter shows how modulation and feedback permit to resolve these difficulties. The results of research confirm the general conclusion of the pioneering research: FCS may transmit signals without coding perfectly, that is in real time, with a bit rate equal to the capacity of systems, and with the limit accuracy of the signals recovery. Moreover, the only difference between the relationships presented in the chapter and those presented in earlier works is the numerical values of modulation index.

The rapidly developing wireless networks (WN) utilize a great number of shortrange low-energy end-node (EN) transmitters. Nowadays, all of them employ the coding and advanced digital technical solutions. The level and number of requirements for EN transmitters grow permanently. However, as noted by many authors, possibilities to improve the performance of the PHY layer of WN are almost exhausted. We discussed this in the beginning of the chapter. Moreover, all networks utilize, on the mass scale, feedback channels.

What can we conclude? Despite its great merits, coding is losing its advantages and is being used in low-power EN transmitters designed for the short-range transmission ("one mile zone" and shorter). The main task of these transmitters is the reliable and secure delivery of relatively small amounts of information to the BSt or master node, if possible, with minimal delay. The great rates (except for rare exclusions) are not necessary: this is the task for BSt which communicate with other BSt or higher level stations.

Today's problems of the EN transmitters design are prosaic: they should be as less energy-consuming as possible to increase the duration of continuous work ("lifetime") and to reduce the requirements of the energy sources. They should be resistant to inter-channel disturbances caused by nearby EN, as well as should have minimal complexity to decrease the production and deployment costs. It is also desirable that they have low emission, small size, light units, etc.

Reduction of the energy consumption inevitably causes the reduction of the power of the EN transmitters and that crucially decreases the quality and range of transmission. Compensation of the losses requires application of more efficient correcting codes and more complex coders, as well as the extension of the channel bandwidth. In turn, wide band transmission creates sufficiently powerful interchannel disturbances in closely placed EN. The result is the appearance of complex technical solutions suppressing these distortions or, vice versa, utilizing them for improvement of the signals recovery. The list of tradeoffs between different requirements of the systems is large, and coding has no efficient answers to these questions.

Having no alternatives, the industry has no other choice but to transfer known principles of long-distance CS with coding (CSC) design and technologies to the design of low-power EN transmitters produced on the scale by the orders greater than powerful CSC transmitters. The not too essential for long-distance communications, constraints on the power of the transmitters, requirements for the bandwidth and other constrains became the crucial considerations in the wireless EN design. From our point of view, the greatest stumbling block is that CSCs do not allow for a development of the systematic approach to their optimization similar to the Bayesian approach described in the chapter. Codes have no parameters permitting their adjustment to the changes of characteristics of the channel, nor allow the formulation of mathematical models accounting for all the transformations of signals as they pass through the transmitter, channel, and receiver. AFCSs do have such possibilities.

*Perfect Signal Transmission Using Adaptive Modulation and Feedback DOI: http://dx.doi.org/10.5772/intechopen.90516*

The main reason for the difficulties was the lack of practical results. Another, less obvious source of failures was the omission of possible saturation of modulators or emitters in the forward transmitters. The not less crucial obstacle also was not discussed in the literature which is the dependence of the CS performance on the

The chapter shows how modulation and feedback permit to resolve these difficulties. The results of research confirm the general conclusion of the pioneering research: FCS may transmit signals without coding perfectly, that is in real time, with a bit rate equal to the capacity of systems, and with the limit accuracy of the signals recovery. Moreover, the only difference between the relationships presented in the chapter and those presented in earlier works is the numerical values of

The rapidly developing wireless networks (WN) utilize a great number of shortrange low-energy end-node (EN) transmitters. Nowadays, all of them employ the coding and advanced digital technical solutions. The level and number of requirements for EN transmitters grow permanently. However, as noted by many authors, possibilities to improve the performance of the PHY layer of WN are almost exhausted. We discussed this in the beginning of the chapter. Moreover, all net-

What can we conclude? Despite its great merits, coding is losing its advantages

Today's problems of the EN transmitters design are prosaic: they should be as less energy-consuming as possible to increase the duration of continuous work ("lifetime") and to reduce the requirements of the energy sources. They should be resistant to inter-channel disturbances caused by nearby EN, as well as should have minimal complexity to decrease the production and deployment costs. It is also

Reduction of the energy consumption inevitably causes the reduction of the power of the EN transmitters and that crucially decreases the quality and range of transmission. Compensation of the losses requires application of more efficient correcting codes and more complex coders, as well as the extension of the channel bandwidth. In turn, wide band transmission creates sufficiently powerful interchannel disturbances in closely placed EN. The result is the appearance of complex technical solutions suppressing these distortions or, vice versa, utilizing them for improvement of the signals recovery. The list of tradeoffs between different requirements of the systems is large, and coding has no efficient answers to these questions. Having no alternatives, the industry has no other choice but to transfer known principles of long-distance CS with coding (CSC) design and technologies to the design of low-power EN transmitters produced on the scale by the orders greater than powerful CSC transmitters. The not too essential for long-distance communications, constraints on the power of the transmitters, requirements for the bandwidth and other constrains became the crucial considerations in the wireless EN design. From our point of view, the greatest stumbling block is that CSCs do not allow for a development of the systematic approach to their optimization similar to the Bayesian approach described in the chapter. Codes have no parameters permitting their adjustment to the changes of characteristics of the channel, nor allow the formulation of mathematical models accounting for all the transformations of signals as they pass through the transmitter, channel, and receiver. AFCSs do have such possibilities.

and is being used in low-power EN transmitters designed for the short-range transmission ("one mile zone" and shorter). The main task of these transmitters is the reliable and secure delivery of relatively small amounts of information to the BSt or master node, if possible, with minimal delay. The great rates (except for rare exclusions) are not necessary: this is the task for BSt which communicate with other

desirable that they have low emission, small size, light units, etc.

scenarios of application.

*Modulation in Electronics and Telecommunications*

modulation index.

BSt or higher level stations.

**20**

works utilize, on the mass scale, feedback channels.

Moreover, the signals generated by the transmitters of CSC are discrete, their form is fixed and in no way depends on the input signals. Information is delivered by combinations of the symbols of code. There is no possibility to regulate the quality of the transmission aside from the external regulation of the power of transmitter or switching the codes. Meanwhile, the quality of transmission provided by the adjusted perfect AFCS depends on the scenario of their application, but always attains the limit or close to the limit values.

General evaluation of the future perspectives of AFCS: currently, almost all CS and networks have feedback channels, and AFCS could solve many of the aforementioned and other problems. Below, we attach a summary of possibilities of the perfect AFCS, which have been established and verified in [36–41] and other works.


8.The FT transmitters can be realized in analog, digital, and mixed technologies. The results of analysis show that the most preferable form of realization would be the software implementation of the FT. Optimal transmissionreception and adjusting algorithms contain all basic information for the development and implementation of the software (SDR) version of the FT. Moreover, this software can be used for the reconfiguration of transmitters and the extension of possibilities of their utilization and functional possibilities of the EN as a whole.

BSt base station

PHY physical layer of network AWGN additive white Gaussian noise

*DOI: http://dx.doi.org/10.5772/intechopen.90516*

*Perfect Signal Transmission Using Adaptive Modulation and Feedback*

MMSE minimal mean square error

SNR signal-to-noise ratio BER bit error rate MSE mean square error

RMS root mean square

**Author details**

Anatoliy Platonov

**23**

provided the original work is properly cited.

Institute of Electronic Systems Warsaw, Warsaw University of Technology, Poland

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: plat@ise.pw.edu.pl; platon945@gmail.com


Most of the listed capabilities of AFCS are not feasible for the CS with coding. In this chapter, we considered only scalar (point-to-point) AFCS which employ the AM transmission, but the theory allows for the extension to optimization of the multi-channel FCS. Moreover, AM is only one of three types of modulation, and each has its own limited operating range. It would be important to investigate the systems with the FM and PM modulations—this could give a new classes of perfect FCS transmitting signals without abnormal errors and with the limit energy-spectral efficiency. It is also worth noting that statistical fitting condition (26) can be used for the optimization of different classes of estimation, controlling, measurement, and signal processing systems.

In conclusion, let us repeat the questions asked in [19]: "Is the PHY layer dead? … whether the research directions taken in the past have always been the right choice and how lessons learned could influence future policy decisions?"
