The document discusses bit error rate (BER), which is defined as the rate at which errors occur during data transmission. BER is calculated as the number of errors divided by the total number of bits sent. It then discusses factors that affect BER such as noise, signal propagation path interference, modulation scheme used, and error correction techniques. The document also provides a MATLAB code example to simulate BER for different signal to noise ratios using BPSK modulation.
The document discusses bit error rate (BER), which is defined as the rate at which errors occur during data transmission. BER is calculated as the number of errors divided by the total number of bits sent. It then discusses factors that affect BER such as noise, signal propagation path interference, modulation scheme used, and error correction techniques. The document also provides a MATLAB code example to simulate BER for different signal to noise ratios using BPSK modulation.
The document discusses bit error rate (BER), which is defined as the rate at which errors occur during data transmission. BER is calculated as the number of errors divided by the total number of bits sent. It then discusses factors that affect BER such as noise, signal propagation path interference, modulation scheme used, and error correction techniques. The document also provides a MATLAB code example to simulate BER for different signal to noise ratios using BPSK modulation.
The document discusses bit error rate (BER), which is defined as the rate at which errors occur during data transmission. BER is calculated as the number of errors divided by the total number of bits sent. It then discusses factors that affect BER such as noise, signal propagation path interference, modulation scheme used, and error correction techniques. The document also provides a MATLAB code example to simulate BER for different signal to noise ratios using BPSK modulation.
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Bit-Error-Rate (BER)
INTRODUCTION
A bit error rate (BER) is defined as the rate at which errors occur in a transmission system. This can be directly translated into the number of errors that occur in a string of a stated number of bits:
BER = number of errors / total number of bits sent
If the medium between the transmitter and receiver is good and the signal to noise ratio is high, then the bit error rate will be very small possibly insignificant and having no noticeable effect on the overall system However if noise can be detected, then there is chance that the bit error rate will need to be considered. Although there are some differences in the way these systems work and the way in which bit error rate is affected, the basics of bit error rate itself are still the same. When data is transmitted over a data link, there is a possibility of errors being introduced into the system. If errors are introduced into the data, then the integrity of the system may be compromised.
The main reasons for the degradation of a data channel and the corresponding bit error rate, BER is noise and changes to the propagation path (where radio signal paths are used). Both effects have a random element to them, the noise following a Gaussian probability function while the propagation model follows a Rayleigh model. This means that analysis of the channel characteristics are normally undertaken using statistical analysis techniques. For fiber optic systems, bit errors mainly result from imperfections in the components used to make the link. These include the optical driver, receiver, connectors and the fiber itself. Bit errors may also be introduced as a result of optical dispersion and attenuation that may be present. Also noise may be introduced in the optical receiver itself. Typically these may be photodiodes and amplifiers which need to respond to very small changes and as a result there may be high noise levels present.
Another contributory factor for bit errors is any phase jitter that may be present in the system as this can alter the sampling of the data. Signal to noise ratios and Eb/No figures are parameters that are more associated with radio links and radio communications systems. In terms of this, the bit error rate, BER, can also be defined in terms of the probability of error or POE. The determine this, three other variables are used. They are the error function, erf, the energy in one bit, Eb, and the noise power spectral density (which is the noise power in a 1 Hz bandwidth), No. It should be noted that each different type of modulation has its own value for the error function. This is because each type of modulation performs differently in the presence of noise. In particular, higher order modulation schemes (e.g. 64QAM, etc) that are able to carry higher data rates are not as robust in the presence of noise. Lower order modulation formats (e.g. BPSK, QPSK, etc.) offer lower data rates but are more robust. The energy per bit, Eb, can be determined by dividing the carrier power by the bit rate and is a measure of energy with the dimensions of Joules. No is a power per Hertz and therefore this has the dimensions of power (joules per second) divided by seconds). Looking at the dimensions of the ratio Eb/No all the dimensions cancel out to give a dimensionless ratio. It is important to note that POE is proportional to Eb/No and is a form of signal to noise ratio.
FACTORS AFFECTING BIT ERROR RATE
It can be seen from using Eb/No, that the bit error rate, BER can be affected by a number of factors. By manipulating the variables that can be controlled it is possible to optimize a system to provide the performance levels that are required. This is normally undertaken in the design stages of a data transmission system so that the performance parameters can be adjusted at the initial design concept stages.
The interference levels present in a system are generally set by external factors and cannot be changed by the system design. However it is possible to set the bandwidth of the system. By reducing the bandwidth the level of interference can be reduced. However reducing the bandwidth limits the data throughput that can be achieved. It is also possible to increase the power level of the system so that the power per bit is increased. This has to be balanced against factors including the interference levels to other users and the impact of increasing the power output on the size of the power amplifier and overall power consumption and battery life, etc. Lower order modulation schemes can be used, but this is at the expense of data throughput. It is necessary to balance all the available factors to achieve a satisfactory bit error rate. Normally it is not possible to achieve all the requirements and some trade-offs are required. However, even with a bit error rate below what is ideally required, further trade-offs can be made in terms of the levels of error correction that are introduced into the data being transmitted. Although more redundant data has to be sent with higher levels of error correction, this can help mask the effects of any bit errors that occur, thereby improving the overall bit error rate.
BER SIMULATION
Here is the Matlab Code For BER Simulation:
N = 10^6 % number of bits or symbols
rand('state',100); % initializing the rand() function randn('state',200); % initializing the randn() function % Transmitter ip = rand(1,N)>0.5; % generating 0,1 with equal probability s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 1 n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; % white gaussian noise, 0dB variance Eb_N0_dB = [-3:10]; % multiple Eb/N0 values for ii = 1:length(Eb_N0_dB) % Noise addition y = s + 10^(-Eb_N0_dB(ii)/20)*n; % additive white gaussian noise % receiver - hard decision decoding ipHat = real(y)>0; % counting the errors nErr(ii) = size(find([ip- ipHat]),2); end simBer = nErr/N; % simulated ber theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))); % theoretical ber % plot close all figure semilogy(Eb_N0_dB,theoryBer,'b.-'); hold on semilogy(Eb_N0_dB,simBer,'mx-'); axis([-3 10 10^-5 0.5]) grid on legend('theory', 'simulation'); xlabel('Eb/No, dB'); ylabel('Bit Error Rate'); title('Bit error probability curve for BPSK modulation'); QUESTIONS a. run the code shown b. Indicate on the lines of code of the simulation process c. Add the lines corresponding to two modulations for WLAN, other than BPSK modulation and show the comparatively d. Comment that has that parameter value and in what situations would have practical application
