Channel Modeling, Fundamentals

Knife Edge Diffraction Model

Diffraction is a phenomenon where electromagnetic waves (such as light waves) bend around corners to reach places which are otherwise not reachable i.e. not in the line of sight. In technical jargon such regions are also called shadowed regions (the term again drawn from the physics of light). This phenomenon can be explained by Huygen’s principle which states that “as a plane wave propagates in a particular direction each new point along the wavefront is a source of secondary waves”.

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Channel Modeling, Fundamentals

Reflection vs Scattering in Ray-Tracing

In ray-tracing simulations one is faced with a complexity at points of intersection between rays and objects. How to handle the reflection, should it be specular or scattered. In this post we consider the two extreme cases; pure reflection vs scattering. For this we consider that in the case of specular reflection the power of the ray is reduced by 3dB (that is R=0.5) and the ray continues as it would if there was no interaction with the object (off course direction would be changed with angle of reflection being equal to angle of incidence). In the case of scattered […]

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Fundamentals

How to Find Point of Intersection of Two Lines

Finding the point of intersection of two lines has many important application such as in Ray-Tracing Simulation.  Two lines always intersect at some point unless they are absolutely parallel, like the rails of a railway track. We start with writing the equations of the two lines in slope-intercept form. y1=b1+m1*x1 y2=b2+m2*x2 Here m1 and m2 are the slopes of the two lines and b1 and b2 are their y-intercepts. At the point of intesection y1=y2, so we have. b1+m1*x1=b2+m2*x2 But at  the point of intersection x1=x2 as well, so replacing x1 and x2 with x we have. b1+m1*x=b2+m2*x or b1-b2=-x*(m1-m2) […]

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Capacity, Fundamentals

Shannon Capacity CDMA vs OFDMA

We have previously discussed Shannon Capacity of CDMA and OFMDA, here we will discuss it again in a bit more detail. Let us assume that we have 20 MHz bandwidth for both the systems which is divided amongst 20 users. For OFDMA we assume that each user gets 1 MHz bandwidth and there are no guard bands or pilot carriers. For CDMA we assume that each user utilizes full 20 MHz bandwidth. We can say that for OFDMA each user has a dedicated channel whereas for CDMA the channel is shared between 20 simultaneous users. We know that Shannon Capacity […]

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Channel Modeling

Sum of Sinusoids Fading Simulator

We have previously looked at frequency domain fading simulators i.e. simulators that define the Doppler components in the frequency domain and then perform an IDFT to get the time domain signal. These simulators include Smith’s Simulator, Young’s Simulator and our very own Computationally Efficient Rayleigh Fading Simulator. Another technique that has been widely reported in the literature is Sum of Sinusoids Method. As the name suggests this method generates the Doppler components in the time domain and then sums them up to generate the time domain fading envelope. There are three parameters that define the properties of the generated signal. […]

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Fundamentals

Noise Calibration in Simulation of Communication Systems

We have been using a wireless signal model in our simulations without going into the details of noise calibration for simulation. In this article we discuss this. Lets assume the received signal is given as r(t)=s(t)+n(t) where r(t) is the received signal s(t) is the transmitted signal and n(t) is the Additive White Gaussian Noise (AWGN). Channel fading is ignored at the moment. Signal to noise ratio for simulation of digital communication systems is given as ρ=Eb/No (1) Where Eb is the energy per bit and No is the noise Power Spectral Density (PSD). We also know that for the case […]

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Channel Modeling, Fundamentals, LTE

Modified Young’s Fading Simulator

In the previous posts we had discussed generation of a correlated Rayleigh fading sequence using Smith’s method [1] and Young’s modification of Smith’s method [2]. The main contribution of Young was that he proposed a mechanism where the number of IDFTs was reduced by half. This was achieved by first adding two length N IID zero mean Gaussian sequences filtered by the filter F[k] and then performing the IDFT on the resulting complex sequence. This was different to Smith’s method where the IDFT was performed simultaneously on two branches and then the outputs of these branches were added in quadrature […]

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BER Performance, Fundamentals, LTE

Theoretical BER of M-QAM in Rayleigh Fading

We have previously discussed the Bit Error Rate of M-QAM in Rayleigh Fading using Monte Carlo Simulation. We now turn our attention to calculation of Bit Error Rate (BER) of M-QAM in Rayleigh fading using analytical techniques. In particular we look at the method used in MATLAB function berfading.m. In this function the BER of 4-QAM, 16-QAM and 64-QAM is calculated from series expressions having 1, 3 and 5 terms respectively. These are given below (M is the constellation size and must be a power of 2). if (M == 4) ber = 1/2 * ( 1 – sqrt(gamma_c/k./(1+gamma_c/k)) ); elseif […]

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Fundamentals, LTE, Solar Energy, WiMAX

Sizing Up a Solar System for a Cellular Base Station

Many operators are thinking of moving from the main grid to alternative energy sources such as wind and solar. This is especially true in third world countries where electricity is not available 24/7 and is also very expensive. This has forced operators to switch their base stations to diesel generators (which is also a costly option). In this article we do a rough estimation of the size a solar system required to run a cellular base station. We start with the assumption that 20 Watts of power are transmitted from a single antenna of base station. For a 3 sector […]

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