COGNITIVE RADIO AND RF COMMUNICATIONS DESIGN OPTIMIZATION USING GENETIC ALGORITHMS

J. F. Hauris, Donya He, Geremy Michel, Cahit Ozbay BAE Systems Electronics & Integrated Solutions, Reston, Virginia 20190

ABSTRACT A communication system must operate in a continuously varying RF environment that depends on multiple parameters that are inter-related and non-linearly coupled. The communication system must be able to adapt to the varying RF conditions. “Cognitive Radios” are being developed to address this issue. This paper discusses the use of Genetic Algorithms (GA) to implement the adaptive processes for a cognitive radio and the associated RF design optimization in a varying RF environment. Specifically GAs are used to solve the optimization of RF parameters for a tactical wireless network. In particular, a Fitness Measure is derived to provide a figure of merit for the performance of the GA in relation to overall RF performance. Additionally, a chromosome structure is derived to consist of “RF genes”. Each gene is a binary string representing some aspect or parameter of the RF environment. Finally the GA determines a set of RF parameters for optimal radio communications in the varying RF environment.

I. INTRODUCTION Tactical RF Communications Systems operate in and travel through varying and changing RF environments. Cognitive radios are being developed to automatically configure the communication system to optimize for and take advantage of the prevailing RF environment. The design of an RF communications link for a particular geographic and network configuration depends on multiple parameters that are non-linearly coupled. For example, operating frequency, receiver noise figure, various antenna types, transmitter power, data rate, interference levels, and modulation / coding scheme are a few of the parameters that must be considered when designing an RF link. These parameters are inter-related and have linear and non-linear coupled relationships and are dependent on interference levels, multi-path fading, and network topology. Trying to obtain a simultaneous optimal solution for these parameter values is a very complex

and difficult task. The solution space for each of the equations governing these parameters varies and overlaps with each other.

One solution to this problem is to apply Evolutionary Computing and in particular Genetic Algorithms (GA). This paper discusses the application of GAs to solve the optimization of the RF parameters for a geographically and RF varying wireless network. In particular, a Fitness Measure (FM, also called a Cost Function) is derived to provide a figure of merit for the performance of the GA in relation to overall RF performance. Additionally, a chromosome structure is derived. This chromosome is constructed of “RF genes”, with each gene consisting of a binary bit string representing some aspect or parameter of the RF environment or the communication system.

The genes used in the present instantiation are: Modulation / Coding Scheme, Gt (transmit antenna gain), Gr (receive antenna gain), Antenna Parameters, receiver NF (noise figure), Pt (transmit power), Data Rate, Coding Gain, Bandwidth, and Frequency. These genes can be thought of as “meters” and “knobs” on a radio. These meters and knobs are adjusted to provide optimal performance. The GA is a method that can determine the optimal settings for these parameters. As the genes vary randomly, a figure of merit is required to guide the GA in its random evolution. This figure of merit (i.e., the Fitness Measure) is the driving force that biases the “natural selection” and “survival” of the candidate genes to provide the most fit and robust genes. The figure of merit is calculated from the Key Performance Parameters (KPPs).

These parameters are used to calculate and determine four Key Performance Parameters (KPPs): Link Margin (LM), C/I (CI), Data Rate (Rb), and Spectral Efficiency (SE). These KPPs were selected because they include and encompass most of the parameters that create an RF environment. These KPPs are then used to create the Fitness Measure. Thus there is a direct chain from randomly varying RF parameters, to system key performance parameters, to the

evolutionary driving force of the Fitness Measure. An integral ingredient for the success of this process

is the proper construction of the Fitness Measure and the genes in order to provide the desired optimization in relation to overall system performance.

II. RF ENVIRONMENT

A. RF Parameters The RF parameters can be divided into two groups:

radio/antenna parameters and environmental parameters. The radio/antenna parameters include values that pertain to radio functioning and include such items as:

1) Frequency of operation 2) Transmission data rate 3) Eb/No, BER 4) Antenna parameters (Gt, Gr, Line Loss, etc) 5) Modulation Type 6) Coding Scheme 7) Coding Gain 8) Signal Bandwidth 9) Transmitted Power 10) Receiver Noise Figure and Noise Temperature The environmental parameters are related to network

layout and geographic topology. The physical environment and the movement of the system through the varying physical environment produce a continuously changing RF environment that is reflected by the following specific items:

1) Interference levels 2) Multi-path fading 3) Tracking loss 4) Propagation Loss 5) Received power levels 6) “Sky” Noise Temperature 7) Link Margin These parameters are not independent and are non-

linearly coupled to each other. For example, frequency of operation affects multiple parameters in both the radio/antenna and environmental groups. Also, parameters such as Eb/No affect other environmental parameters (such as Link Margin and Interference levels) and is affected by other radio parameters such as Coding scheme, Modulation type, and bandwidth.

Thus from this small sampling of interactions it can be seen that the simultaneous solution of these parameters involves multiple linear and non-linear coupled and overlapping solution spaces. The

optimization of these parameters would involve a large combination of equations. There is no standard method of guaranteeing an optimal solution.

B. Fitness Measure In order to solve this optimization problem,

Evolutionary Computing methods and in particular Genetic Algorithms (GA) were investigated as possible solutions. Rieser [1], [2] reported using GAs to determine the optimization of wireless channel models and certain aspects of the wireless communication system. Based on this work it was determined that a Fitness Measure (FM, or Cost Function) needed to be derived. This FM is critical in the success of the GA. The purpose of the FM is to drive the random processes of the GA in the desired direction to optimize the parameters for performance.

Key Performance Parameters (KPPs) were chosen to represent measures of how well the system is performing. The following values were determined to provide a good indication of overall system performance:

1) Link Margin 2) Spectral Efficiency 3) Data Rate 4) C/I (Received Carrier Power / Interference

level) These values were chosen because they encompass

all of the radio and environmental parameters. Many of the parameters are used to determine multiple KPPs and can have coupled and opposing effects. These relations will be discussed later. Link Margin measures how close to failure the system is. It is a critical measurement and can be related to many operational parameters. Spectral Efficiency tells how well the channel and radio parameters are being used. C/I represents a strong relationship of radio parameters to environmental parameters. And finally, data rate is critical to overall system performance.

These KPPs were then used to develop the FM. It was decided that a maximum value of FM was best as this avoided divide-by-zero problems. System performance is maximized when the KPPs are maximized. Thus the largest Link Margin, Spectral Efficiency, Data Rate, and C/I provide the best system performance. However, even though it is critical that the Link Margin criteria be met, one does not want to optimize that value at the expense of data rate or C/I. Therefore a weighting is assigned to each KPP. The following equation will be maximized for maximal KPPs.

)}()()(){( 4321 CIwRbwSEwLMwFM ×+×+×+×=

where and ,10 →=iwLM = Link Margin SE = Spectral Efficiency Rb = Data Rate CI = C/I Thus by weighting each KPP and maximizing their

value, an optimum FM can be determined. The next problem is to relate the KPPs to the radio/antenna and environmental parameters and then to relate those parameters to the genes and a chromosome structure for the genetic algorithm.

III. RELATION OF GENES TO KPPS AND FM

A critical issue is to relate the above RF parameters to a gene and chromosome structure for insertion into the genetic algorithm. Finally, a relation between the genes and the fitness measure must be established.

A. Input Parameters Before defining the genes, it must be noted that there

are two input parameters. These are values that are established by the system user and are employed to set the bounds of system performance. These parameters are: BW = signal bandwidth, BER = system bit error rate. These are not values to be optimized, but set the limits for the RF parameters and establish a minimum level of required system performance.

B. Genes for Rb and SE The critical RF parameters have been identified for

optimization. The key performance parameters have been selected and these have been used to derive a fitness measure function. Genes must now be developed that can be incorporated into the genetic algorithm. The function of the genes is to provide a random and varying population of candidate values that can be used to set the radio system parameters. The fitness of these genes is determined by the FM. Therefore, a translation or encoding must be developed between the KPPs and appropriate genes.

The genes can be developed by writing out the chain of equations for the KPPs and tracing out the fundamental variables that can be varied.

For the RF parameter “Rb” (data rate), the gene

becomes Rb itself. This is because Rb cannot be broken down into a more fundamental measurement.

The equation for SE (Spectral Efficiency) is simply:

,RbGC

BWSE×

=

where BW = Bandwidth is a user input, and GC = Coding Gain and Rb are the remaining variables for genes.

C. Genes for CI The following figure depicts the equations for CI

and shows how the genes (designated as bold, italicized, and underlined) fall out as fundamental variables for this parameter.

Figure 1. Flow of equations for CI that elaborates the relationship of the KPP to the fundamental variables which become the genes. Genes are designated by bold, italicized, and underlined words.

It can be seen that CI incorporates environmental

interference levels (that are determined from the interferers and jammers in the network geographic layout) and the received carrier level, C. C is a function of EIRP (Equivalent Isotropic Radiated Power), Gr (receiver antenna gain), and environmental losses of signal power. These can be reduced further to:

Pt – Transmitter power level Gt – Transmit antenna gain Gr – Receive antenna gain AP – Antenna parameters (Line Loss, etc.) FR – Frequency These variables then become the genes associated

with this KPP.

D. Genes for Link Margin (LM) The final KPP is LM. The Link Margin depends on

a large number of parameters and is determined

CI = C / I

Interference Level

Frequency EIRP + G - Losses

Pt x Gt Gr

Losses = (Prop Loss) + (Multi-path Loss) + (Tracking Loss) + (Axial Ratio Loss)

System Input, dependent on network geographic layout. Determined via Geo-location

Antenna Parameters

through multiple steps as outlined in figure 2. Link Margin is the difference between required and

actual signal energy normalized to thermal noise. The required Eb/No is determined by the input value for desired BER and the type of modulation and coding scheme used by the radio. The actual Eb/No is dependent on multiple system and environmental factors such as: system noise temperature, signal power levels, and environmental losses. These are delineated in Figure 2. The fundamental variables have much in common with the CI genes and can be identified as:

MC – Modulation / Coding Scheme NF – system noise figure Pt – Transmitter power level Gt – Transmit antenna gain Gr – Receive antenna gain AP – Antenna parameters FR – Frequency Rb – Data rate Many of these genes are the same as those

previously determined. This indicates the inter-relationship and coupling among the various KPPs and RF parameters. For LM, NF is a new gene. This gene is the noise figure of the radio and thus is a figure of merit for the radio. This value depends on the LNA (Low Noise Amplifiers) and other radio circuits as well as radio architecture and receive antenna noise temperature. Gt, Gr, and Line Loss (antenna-amp loss) are also parameters related to radio/antenna hardware.

It may be noted that these parameters are not capable

of taking on random values but are fixed by the hardware. This puts a limitation on the use of these parameters as genes. However, a number of systems exist that have multiple radios and antennas in them. A choice must be made as to which of the radios and antennas combination to use. The GA can be of assistance in this selection. This puts a limitation on the values which the GA can attribute to these genes. Either the GA will only permit these genes to take on realistic values or it will discard (via a zeroed FM) any values that cannot be instantiated.

Finally “MC” is the Modulation / Coding scheme

that is employed by the radio. Many new radios are Software Defined Radios (SDR). These radios have their functions incorporated in software and can download many different types of schemes as required. This is a significant parameter to control for system optimization and incorporates much of the physical layer signal processing and communications protocols.

Figure 2. Flow of equations for LM that elaborates the relationship of the KPP to the fundamental variables which become the genes. Genes are designated by bold, italicized, and underlined words.

IV. GENES AND CHROMOSOMES

A. Genes and Chromosome Structure The above analysis results in the following list of

genes that provide the source of random variation for the KPPs. These genes when combined together form a chromosome for the genetic algorithm.

MC – Modulation / Coding Scheme NF – Noise Figure Pt – Transmitter power level Gt – Transmit antenna gain Gr – Receive antenna gain AP – Antenna parameters FR – Frequency Rb – Data rate GC – Coding Scheme These variables are set to a population of random

values (within bounds) and cranked through the above equations. The above equations provide the KPPs that are then used to calculate the respective fitness measure for each chromosome in the population. The genetic algorithm uses this information to select and breed further generations and come to an optimized solution.

B. Constraints on gene values The gene variables must be related to physically

realizable instantiations of radio and RF parameters. Additionally, not all radios have the same range of

LM = Eb/No(req’d) – Eb/No(calc’d)

Modem Coding Type

BER

C x 1

No Rb

EIRP + G/Tsys – K – (Prop Loss) – (Multipath Loss) – (Tracking Loss) – (Axial Ratio Loss)

Pt x Gt Gr – 10log(Tsys) - AntAmpLoss

Gr – 10log[ Tant + To(10^(NF/10) -1) ] - AntAmpLoss

Antenna Parameters

Frequency Prop Loss Multipath Loss Tracking Loss Axial Ratio Loss Gt Gr

capabilities. Therefore, care must be taken to ensure that mutually exclusive random variations are not considered. For example, if a physical radio is capable of transmitting 25 kHz – 100 kHz, it must be ensured that the “Rb” gene for this instantiation does not include values outside of this range. Care also must be taken to ensure this does not occur in crossover breeding and mutation. The software could check to throw away any of these genes. However, this impacts software performance. An alternative method is available that permits all variations. However when the fitness measure is calculated, these “monster” mutations are recognized and receive a very low or zero fitness level. They are thus bred out rather quickly.

V. GENETIC ALGORITHM SPECIFICS

The genetic algorithm is a basic form [3], [4] employing single crossover breeding at random locations within the chromosome. A mutation rate of 0.001 was used and applied on a bit by bit basis. The “roulette wheel” algorithm was used to determine the natural selection of each generation based on its fitness measure. A general population of 100 chromosomes was chosen with a breeding duration of 50 to 100 generations. The solution typically converged in less than 50 generations.

VI. RESULTS

For verification of operation the genetic algorithm was modeled using realistic radio and RF parameters. Numerous simulations were run and results verified. The output consisted of final optimized gene values.

The following types of modulation schemes were used in the model:

1) Non-coherent (OOK, FSK, MSK) 2) Bi-polar 3) Uni-polar (FSK, PAM, ASK) 4) DPSK 5) Polar (BPSK, QPSK, MSK, PAM)

The polar modulation schemes have the best BER

performance characteristics. However, a genetic algorithm is not intended to find the best but rather one of the best, and to balance this selection with the other parameters. As a result, the following is a short list of some of the obtained values. It can be seen that the “polar” method was not always chosen. When alternative modulation schemes were chosen, it was

because that particular configuration had higher data rates or higher received signal power level. Thus, the system was optimized for all parameters.

Modulation BER rating Bit Rate Rcvd Signal Polar 1 111 Kbps -89 dB DPSK 2 127 Kbps -87 dB Uni-polar 3 127 Kbps -83 dB Non-Coh 4 127 Kbps -85 dB

(The reason that the last three schemes have the

same bit rate was because of the quantization of the gene bit string. If more bits had been used, a finer resolution would have resulted. These values were accepted as a verification of the method.)

Finally, the average and maximum fitness measure values were plotted for each run. Figures 3 and 4 show two typical results. As can be seen, the average FM value starts out low and progressively increases, indicating improvement as the generations proceed. Eventually they level off. The maximum fitness measure starts at a higher (but not maximal) level and also slowly increases as the generations proceed. This also confirms that the genetic algorithm is breeding improved populations at each generation. It should be noticed that the average FM increases in a smooth manner reflecting the gradual nature of the general improvement of the population. However the maximum fitness measure has generations were some individual(s) have a significant improvement. These “genius” chromosomes are captured and saved via elitism. At each stage, the five best (in FM terms) members are saved and are guaranteed propagation through the next generation. This ensures that these elite members are carried forward. During the run, the maximum FM and its associated chromosome are tracked and saved. At the end of the trial, this best member is used for the optimal solution.

VII. CONCLUSION

KPPs were derived for a radio / RF environment. An FM was developed that reflected how well these key performance parameters predicted an optimal radio setting. Genes were developed from radio and environmental RF parameters. These genes were used to calculate the KPPs, which were then used to determine the fitness measure. Thus basic radio and RF parameters are related to genetic algorithm values (genes and its chromosome). These genes were

incorporated into a basic genetic algorithm that produced an optimal set of genes according to the fitness measure. These genes reflected back to the radio and RF values and provided optimal settings for a radio and communication system in a specific RF environment. The entire system was verified on simulation and is being incorporated into a system.

Figure 3. Typical result for average and maximum fitness measure values for a run through 100 generations. Each generation consisted of 100 chromosomes.

Figure 4. Typical result for average and maximum fitness measure values for a run through 100

generations. Each generation consisted of 100 chromosomes.

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