Fundamentals, Solar Energy

Calculate Solar Panel Tilt

1. Find the direction of magnetic North and consequently magnetic South. 2. Adjust for magnetic declination to find exact true South. 3. Point solar panels towards true South. 4. Find optimum tilt angle based on the latitude and the season. Enter the value of latitude below to find the panel tilt in degrees. Winter Latitude *+ = Degrees Spring and Fall Latitude *– = Degrees Summer Latitude *– = Degrees   Note: 1. The result above is the angle in degrees from the horizontal. 2. If you do not know the latitude of your city you can look it up […]

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Capacity, Fundamentals, LTE

Does Shannon Capacity Increase by Dividing a Frequency Band into Narrow Bins

Somebody recently asked me this question “Does Shannon Capacity Increase by Dividing a Frequency Band into Narrow Bins”. To be honest I was momentarily confused and thought that this may be the case since many of the modern Digital Communication Systems do use narrow frequency bins e.g. LTE. But on closer inspection I found that the Shannon Capacity does not change, in fact it remains exactly the same. Following is the reasoning for that. Shannon Capacity is calculated as: C=B*log2(1+SNR) or C=B*log2(1+P/(B*No)) Now if the bandwidth ‘B’ is divided into 10 equal blocks then the transmit power ‘P’ for each […]

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Channel Modeling, Fundamentals

Uniform, Gaussian and Rayleigh Distribution

It is sometimes important to know the relationship between various distributions. This can be useful if there is a function available for one distribution and it can be used to derive other distributions. In the context of Wireless Communications it is important to know the relationship between the Uniform, Gaussian and Rayleigh distribution. According to Central Limit Theorem the sum of a large number of independent and identically distributed random variables has a Gaussian distribution. This is used to model the amplitude of the in-phase and quadrature components of a wireless signal. Shown below is the model for the received […]

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Fundamentals

Fading Model – From Simple to Complex

1. The simplest channel model just scales the input signal by a real number between 0 and 1 e.g. if the signal at the transmitter is s(t) then at the receiver it becomes a*s(t). The effect of channel is multiplicative (the receiver noise on the other hand is additive). 2.   The above channel model ignores the phase shift introduced by the channel. A more realistic channel model is one that scales the input signal as well rotates it by a certain angle e.g. if s(t) is the transmitted signal then the received signal becomes a*exp(jθ)*s(t). 3. In a realistic […]

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BER Performance, Fundamentals, LTE, Modulation, WiMAX

M-QAM Bit Error Rate in Rayleigh Fading

We have previously discussed the bit error rate (BER) performance of M-QAM in AWGN. We now discuss the BER performance of M-QAM in Rayleigh fading. The one-tap Rayleigh fading channel is generated from two orthogonal Gaussian random variables with variance of 0.5 each. The complex random channel coefficient so generated has an amplitude which is Rayleigh distributed and a phase which is uniformly distributed. As usual the fading channel introduces a multiplicative effect whereas the AWGN is additive. The function “QAM_fading” has three inputs, ‘n_bits’, ‘M’, ‘EbNodB’ and one output ‘ber’. The inputs are the number of bits to be passed […]

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BER Performance, Fundamentals, LTE, Modulation, WiMAX

M-QAM Bit Error Rate in AWGN

Quadrature Amplitude Modulation has been adopted by most wireless communication standards such as WiMAX and LTE. It provides higher bit rates and consequently higher spectral efficiencies. It is usually used in conjunction with Orthogonal Frequency Division Multiplexing (OFDM) which provides a simple technique to overcome the time varying frequency selective channel. We have previously discussed the formula for calculating the bit error rate (BER) of QAM in AWGN. We now calculate the same using a simple Monte Carlo Simulation. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % FUNCTION THAT CALCULATES THE BER OF M-QAM IN AWGN % n_bits: Input, number of bits % M: Input, constellation […]

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Fundamentals

Fast Fourier Transform – Code

Most of us have used the FFT routine in MATLAB. This routine has become increasingly important in simulation of communication systems as it is being used in Orthogonal Frequency Division Multiplexing (OFDM) which is employed in 4G technologies like LTE and WiMAX. We would not go into the theoretical details of the FFT, rather, we would produce the MATLAB code for it and leave the theoretical discussion for a later time. The underlying technique of the FFT algorithm is to divide a big problem into several smaller problems which are much easier to solve and then combine the results in […]

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Fundamentals

Detecting Sinusoids in Noise

We have previously discussed the problem of detecting two closely spaced sinusoids using the Discrete Fourier Transform (DFT). We assumed that the data set we got was pure i.e. there was no noise. However, in reality this is seldom the case. There is always some noise, corrupting the signal. Let us now see how it effects the detection problem. We consider Additive White Gaussian Noise (AWGN) as the corrupting source. The noise power is set equal to the power of the two sinusoids i.e. we have an SNR of 0 dB. This is quite a severe case, the noise power […]

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