Fading – RAYmaps

October 7, 2022December 9, 2024Antennas, Capacity, Channel Capacity, Fundamentals

Why is MIMO Fading Capacity Higher than AWGN Capacity

From linear algebra we know that to find four unknowns we need four independent equations. There is no way we can find the values of A, B, C and D from the above equations. To simplify the above equations we have removed AWGN but even in presence of AWGN we will have the same predicament. This shows that in the absence of fading there is no multiplexing gain however high the Signal to Noise Ratio is (in the above example SNR is infinite).

September 28, 2022December 9, 20245G, Antennas, Capacity, Fundamentals

MIMO, SIMO and MISO Capacity in AWGN and Fading Environment

In a previous post we had discussed MIMO capacity in a fading environment and compared it to AWGN capacity. It sometimes feels unintuitive that fading capacity can be higher than AWGN capacity. If a signal is continuously fluctuating how is it possible that we are able to have reliable communication. But this is the remarkable feature of MIMO systems that they are able to achieve blazing speeds over an unreliable channel, at least theoretically.

January 13, 2020June 3, 2022BER Performance, Modulation

Orthogonal Minimum Shift Keying (OMSK)

Some Background Before we delve deep into Minimum Shift Keying (MSK) and its performance in presence of co-channel interference the reader is advised to look at the following posts. Post 1 – MSK BER performance in AWGN and flat fading environment when viewed as extension of BPSK Post 2 – MSK Power Spectral Density and its BER performance in AWGN when viewed as a CPM Post 3 – MSK BER Performance in AWGN and flat fading environment when viewed as a CPM Co-channel interference is a phenomenon widely encountered in wireless communication systems and the main reason for that is […]

December 18, 2019June 4, 2022BER Performance, Modulation

MSK – A Continuous Phase Modulation (CPM)

Some Background on MSK I – In the previous post we presented the mathematical model and code for BER calculation of a popular modulation scheme called MSK. However in the code we shared, we only considered one sample per symbol, which makes MSK look like BPSK. While BPSK symbols fall on the real axis, MSK symbols alternate between real and imaginary axes, progressing by π/2 phase during each symbol period. MSK signal thus has memory and this can help in demodulation using advanced techniques such as Viterbi Algorithm.

December 10, 2019June 4, 2022BER Performance, Modulation

Minimum Shift Keying Bit Error Rate in AWGN

Minimum Shift Keying (MSK) is a type of Continuous Phase Modulation (CPM) that has been used in many wireless communication systems. To be more precise it is Continuous Phase Frequency Shift Keying (CPFSK) with two frequencies f1 and f2.

March 31, 2019June 4, 2022Channel Modeling, Fundamentals

Wireless Channel Modeling: Back to Fundamentals

When a wireless signal travels from a transmitter (Tx) to a receiver (Rx) it undergoes some changes. In simple terms the signal s(t) is scaled by a factor h(t) and noise n(t) is added at the receiver.

August 22, 2017August 22, 2017Channel Modeling, Fundamentals, LTE

Rayleigh Fading Envelope Generation – Python

When wireless signals travel from a transmitter to a receiver they do so after reflection, refraction, diffraction and scattering from the environment. Very rarely is there a direct line of sight (LOS) between the transmitter and receiver. Thus multiple time delayed copies of the signal reach the receiver that combine constructively and destructively. In a sense the channel acts as an FIR (finite impulse response) filter. Furthermore since the transmitter or receiver may be in motion the amplitude and phase of these replicas varies with time. There are several methods to model the amplitude and phase of each of these […]

July 16, 2017July 17, 2017BER Performance, Fundamentals

Alamouti – Transmit Diversity Scheme – Implemented in Python

We have already seen in previous posts that the BER of BPSK increases significantly when the channel changes from a simple AWGN channel to a fading channel. One solution to this problem, that was proposed by Alamouti, was to use Transmit Diversity i.e. multiple transmit antennas transmit the information over multiple time slots increasing the likelihood of receiving the information. We have considered the simplest case of two transmit antennas and BPSK modulation (QPSK modulation would give the same BER with twice the throughput). Given below is the Python code for this, feel free to modify it and run it […]

July 10, 2017July 10, 2017BER Performance, Fundamentals

Python Code for BPSK BER in Rayleigh Fading

We have previously calculated the bit error rate of BPSK in an AWGN channel, we now do the same for a Rayleigh fading channel. Remember that we have now shifted our focus from MATLAB to Python since its open and free to use. We are currently using Python-2 but intend to Python-3 once some integration issues with Trinket are sorted out.