Chapter 4 Communication System Design and Parameters
CHAPTER 4 COMMUNICATION SYSTEM DESIGN AND PARAMETERS 4.1. Introduction In this chapter the design parameters and analysis factors are described which were used while designing of proposed error control code for communication system. Performance measure parameters and communication channel parameters are presented. SNR and its variants and relationship among them are derived. AWGN channel parameters and default values of these are presented and at last of this chapter signal power consumption estimation are given. 4.2. Communication System Design Components Every communication system consist a transmitter and receiver joined via several communication entities like source encoder, channel encoder, modulator etc. These entities have been described in chapter 1. The channel encoder is used to append the parity bits and channel decoder find out errors in received block. Communication channel is exposed to noise sources which can alter the bits or signals transmitted through this channel. For avoiding from exposing to noise; signals are sent at high power in compare with noise signals. In the proposed communication system error correction codes are used so that signals can be sent at low power. The use of error correction code avoids the data damage and loss. This thesis is focus on error correction code so in this thesis mainly work done on designing of error correction code. In chapter 5 the detailed designing of encoder and decoder for block codes are given. In chapter 6 designing of 37
convolutional encoder and decoder are given and BER performances of both codes were calculated. Information Source Error Control Coding Modulation Noisy Communication Channel Information Receiver Error Control Decoding Demodulation Figure 4.1 Components and Steps in Communication System Error Control Coding Error-control coding is a mechanism in which redundancies bits are added into data to be transmitted so that receiver can detect or correct some of the errors. These are two types: Block code: In this code the information/message bits and error control bits are in separate blocks. Before encoding decoding process first data are compiled into blocks. The message bits are divided into k size blocks and then encoding is performed. Convolutional code: Convolutional codes are alternatives to block coding in which encoding and decoding can take place on a continuous data bit stream instead of static block 38
as was in block codes. A continuous bit stream is converted into a single codeword which is also a bit stream. 4.3. Communication System Analysis Parameters There are some considerations which have to be taken while designing the communication system. The system has many parameters and factors which affect the performance of communication system. In this section related to error control code and communication system; some important design considerations and analysis factors are described. 1. Redundancy: The inclusion of extra error controlling bits which are necessary to append with the message bits for detection and correction the errors. These bits are calculated by predefined mathematical rules known as encoding process. More redundancy bits have more error correction capabilities if an optimized encoding algorithm is used. High redundancy requires high bandwidth so while designing an error correction code it was focused that with low redundancy; maximum number of errors must be corrected. 2. BER: In digital communication BER is defined as the ratio of number of bit errors to the total number of transferred bits during a studied time interval. During the transmission, number of bits in communication channel has been altered due to noise, interference, distortion or bit synchronization errors. While designing a communication system or error control code it was focused that BER must be minimized. 3. Extensibility: The communication system or error control code can be expanded, and improved when required and error correction capabilities could be increased. 39
4. Modularity: The communication system consists of individual blocks in its construction and every module or entity treats the incoming bits or signals from one module to the other as an output source. 5. Usability: The error control code widely designed for space and satellite communication but it can be in mobile communication systems and in other communication networks. 4.3.1. Performance Analysis Factors To evaluate the performance of error correcting code, several performance measure metrics such as error correction capability, encoding decoding delay and error controlling bit overhead are commonly used. The analysis of error correcting codes can be done on the basis of hardware and software performance of the codes. 4.3.2. Hardware Parameters This analysis is performed on hardware or simulator. For hardware performance of the code following parameters can be considered: 1. Probability of Uncorrected Errors. 2. Signal Power Consumption 3. Encoding/ Decoding Delay 4. Encoder/ Decoder Hardware Complexity 5. Number of Hardware Components The error correcting codes can be analyzed on the basis of overhead (in terms of redundant bits) and error correction capabilities of codes. The term overhead is used to describe the redundant bits. More overhead requires more bandwidth. For example, maintaining an audit trail might result in 10% overhead, meaning that the program will run 10% slower when the audit trail 40
is turned on. Programmers often need to weigh the overhead of new features before implementing them. 4.3.3. Software Parameters When to design hardware encoder is very complex and costly then software based encoding decoding is used. This uses some encoding decoding algorithm and calculates the parity bits (overhead). A good error correction method has low overhead and better error correction capabilities. The performance analysis of error correcting codes can be performed on the basis of software parameters. The analysis parameters are:- 1. Overhead (Error Control Bits) 2. Encoding/Decoding delay 3. Bit Error Ratio (BER) 4. Energy/bit(E b ) and E b N 0 4.4. Transmit Power and Error Control Coding Concept of transmit power is used with respect to distance, less distance requires less transmit power while large distance requires greater transmit power. Similarly, Error Control Codes are used for efficient data transmission, Block Codes or Convolutional Codes are types of them. Signal transmitted with minimum power is an efficient source of energy minimization. Receiver has to maintain a minimum signal to noise power called E b N 0 for successful operation. Transmit power required to transmit a signal represented by P tx in free space model is given by (1)...(1) 41
.. (2) Here, E b is minimum energy that is required for one bit where N 0 is noise power spectral density, is spectral efficiency expressed as information rate to bandwidth ratio, m noise proportionality constant, K Boltzman constant and T absolute temperature all together represents signal noise represents transmitted wavelength at some distance represented by d in free space model. Transmitted power of signal depends on distance between transmitter and receiver. If it is short then less transmit power is required and if it's large then signal has to be transmitted with maximum power. When distance is greater than sometimes data needs to be retransmitted by using some FEC code. So that actual data should be sent and received with in time. Additional parity bits are appended with information bits for receiving exact information that was originally transmitted. For example, information or message that is being sent is m of length k and extra parity bits are r added to information bits m to form a codeword c, these extra redundant bits enables decoder to correctly decode c. When data is sent through a noisy channel where error occurring chances are high then error correction code minimize the errors and low BER may be obtained at lower SNR value. Difference between SNR levels to reach a certain BER value in coded and un-coded system is called coding gain. Required transmit power is divided by transmission rate which is equal to energy required per bit. For calculating this power consumed by data or total information bits which are being transmitted is divided by total bits. Energy per bit required for transmitting data by un-coded system and that for coded system is calculated from given formulas. Where coded data transmission requires code gain values for energy calculation. 42
...(3.1) (3.2) Eq. (3.3) below gives energy saving from either coded or un-coded data transmission (3.3) Signal to Noise Ratio (SNR) In the previous chapters model of communication system already has been studied and the aim of this thesis is to minimize signal power consumption by using error control coding. The performance of different error control coding schemes in the presence of noise will be measured in terms of the signal-tonoise ratio (SNR) at the output of the receiver, defined as SNR = average power of message signal at the receiver output/average power of noise at the receiver output. E b /N 0 is another important parameter in digital communication which normalizes SNR into SNR per bit. This parameter is used in performance measurement of error control code in terms of BER. It is a ratio of energy per bit to noise power spectral density, where E b is the signal energy associated with each user data bit. It is calculated by signal power divided by user bit rate, unit of it is joules if signal power in watts and bit rate in bits/second. N 0 is the noise spectral density, measured in watts per hertz or joules. The channel distorts the signal, and noise accumulates along the path. Worse yet, the signal strength decreases while the noise level increases with distance from the transmitter. Thus the SNR is continuously decreasing along the length of the channel. Amplifiers will increase both the signal and the noise, and may indeed introduce more noise of their own. 43
4.5. Signal Power Consumption Estimation While designing of most digital communications systems one or more these factors are considered: bandwidth efficient, power efficient, or cost efficient. Power efficiency describes the ability of the system to reliably send information at the lowest practical power level. For calculating power consumption Matlab simulation was used. Messages were transmitted without error control code and with error control code. On the same BER the signal power was measured that is the power gain obtained by error control code. The signals were transmitted through AWGN channel and then white Gaussian noise was added. Without using error control code some value of E b /N 0 was set and after using error control code lower value of E b /N 0 was set and then power gain was calculated. In the AWGN channel some parameters were set manually and remaining was taken by default values. 4.5.1. Signal Power and Power Gain A signal is a single-valued function of time that conveys information from source to receiver and at every point in time has a unique value and this value may either be a real number, or a complex number. It may be analog or digital, an analog signal is a continuous function of time, for which the amplitude is also continuous and it arises whenever a physical waveform is converted to an electrical signal. A digital signal is a discrete function of time, for which the amplitude can only have a finite set of values. Sometimes a distinction is also made of discrete-time signals these are signals that are a discrete function of time, but the amplitude may take on a continuum of values. The instantaneous power of a voltage or current signal is given by P = v(t) 2 / R or P = i(t) 2 R, where R is the resistance. 44
Signal Power Gain is defined as the reduction in Es/N 0 permissible for a coded communication system to obtain the same probability of error as an un-coded system. 4.5.2. Relationship between SNR and E b N 0 The relationship between E b /N 0 and SNR have several forums, whether SNR and E b /N 0 are same or not, the relationship is very easier to understand. Let s start with the basic equation and try to verify its authenticity. S/R b = E b (1) where, R b = bit rate in bits/second E b = Energy per bit in Joules/bit S = Total Signal power in Watts As it is known from fundamental physics that Power = Energy/Time. Using SI units, let s verify the above equation. S/R b = E b Watts bitssecond = Joulesbit Wattsbitssecond = Joulesbit Watts = Joulessecond This verifies the power, energy relationship between Ss and E b. Now, introducing the noise power N 0 in equation (1) E b N 0 = S(R b N0) SNR = (R b E b )/N 0 (2) This equation implies that the SNR will be more than E b N 0 by a factor of R b (if R b > 1 bit/second). 45
Increasing the data rate will increase the SNR, however, increasing R b will also cause more noise and noise term also increases (due to ISI intersymbol interference, since more bits are packed closer and sent through the channel). So SNR cannot be increased by simply increasing R b. This must strike a compromise between the data rate and the amount of noise that a receiver can handle. 4.6. AWGN Channel Parameters In practice, the digital signal is still transmitted by analogue waveforms. Although the noise applied to the transmission waveforms takes many forms, they are all analogue in manner one way or the other. Additive White Gaussian Noise (AWGN) channel model is a basic noise model which is generally accepted model for communication. It adds white noise with a constant spectral density (expressed as watts per hertz of bandwidth) and a Gaussian distribution of amplitude in transmitted signals. The AWGN Channel adds real Gaussian noise and produces a real output signal when input is complex signal then output also complex signal. In the AWGN channel a variable number of parameters can be set. The parameter names and its values are given and if not provided then default values are taken automatically. hchan = comm.awgnchannel (Name1, Value1,..., NameN, ValueN); it creates an AWGN channel object hchan with specified arguments. The following parameters (arguments) can be specified and given values for an AWGN channel. NoiseMethod: - It is used for specifying noise level as one of Eb/No, Es/No, SNR, and variance. The default argument is Eb/No. 46
EbNo: - It is energy per bit to noise power spectral density ratio and it is unit less entity that is given in decibels and its default value is 10. EsNo: - It is energy per symbol to noise power spectral density ratio and it is also unit less entity that is given in decibels and its default value is also10. SNR: - It is signal to noise ratio which is a numeric or real value applies when NoiseMethod properties is used. Its default value is 10. BitsPerSymbol: - It is number of bits which are assigned to each input symbol when noise method property is set to Eb/No and its default value is 1 bit. SignalPower: - it specifies the mean square power of the input signal in Watts and it is applied when noise method is used. The default value is 1 and nominal impedance is 1 Ω. SamplesPerSymbol: - It specifies the number of samples per symbol and its default value is 1. 4.7. Results and Conclusion In this chapter communication system design parameters and analysis factors for error control code were described. Transmit power and its estimation in E b N 0 and EsN 0 were derived. The relationship between SNR and its variants were presented. The common parameters used in MATLAB for chapter 5 and 6 were presented and AWGN channel common parameters were set and its default values were elaborated. 47