Error Probability Performance For Bpsk
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Bit Error Probability For Bpsk
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Probability Of Error In Qpsk
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Bit-error-probability-for-bpsk-modulation
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an optimum BPSK receiver in AWGN channel (4 votes, average: 5.00 out of 5) Loading... BPSK modulation is the simplest of all the M-PSK techniques. An insight into the derivation of error rate performance of probability of error for bpsk and qpsk an optimum BPSK receiver is essential as it serves as a stepping
Calculate Probability Of Error For Bpsk
stone to understand the derivation for other comparatively complex techniques like QPSK,8-PSK etc.. Understanding the concept of Q function probability of bit error formula and error function is a pre-requisite for this section of article. The ideal constellation diagram of a BPSK transmission (Figure 1) contains two constellation points located equidistant from the origin. Each constellation http://ieeexplore.ieee.org/iel5/7/17457/00805454.pdf point is located at a distance $latex \sqrt{Es} $ from the origin, where Es is the BPSK symbol energy. Since the number of bits in a BPSK symbol is always one, the notations – symbol energy (Es) and bit energy (Eb) can be used interchangeably (Es=Eb). Assume that the BPSK symbols are transmitted through an AWGN channel characterized by variance = N0/2 Watts. When http://www.gaussianwaves.com/2012/07/intuitive-derivation-of-performance-of-an-optimum-bpsk-receiver-in-awgn-channel/ 0 is transmitted, the received symbol is represented by a Gaussian random variable ‘r' with mean=S0 = $latex \sqrt{Es} $ and variance =N0/2. When 1 is transmitted, the received symbol is represented by a Gaussian random variable – r with mean=S1= $latex \sqrt{Es} $ and variance =N0/2. Hence the conditional density function of the BPSK symbol (Figure 2) is given by, Figure 1: BPSK - ideal constellation Figure 2: PDF of BPSK Symbols $latex \begin{matrix} f(r\mid 0_T)=\frac{1}{\sqrt{\pi N_0}}exp\left \{ -\frac{\left( \hat{r}-\hat{s}_0\right )^2}{N_0} \right \} \;\;\;\;\;\rightarrow (1A) \\ \\ f(r\mid 1_T)=\frac{1}{\sqrt{\pi N_0}}exp\left \{ -\frac{\left( \hat{r}-\hat{s}_1\right )^2}{N_0} \right \}\;\;\;\;\;\rightarrow (1B) \end{matrix} &s=1&fg=0000A0$ An optimum receiver for BPSK can be implemented using a correlation receiver or a matched filter receiver (Figure 3). Both these forms of implementations contain a decision making block that decides upon the bit/symbol that was transmitted based on the observed bits/symbols at its input. Figure 3: Optimum Receiver for BPSK When the BPSK symbols are transmitted over an AWGN channel, the symbols appears smeared/distorted in the constellation depending on the SNR condition of the channel. A matched filter or that was previously used to construct the BPSK symbol
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