BER Performance – Page 2

November 26, 2019June 4, 2022BER Performance, Fundamentals, Simulation

Pulse Amplitude Modulation Symbol Error Rate in AWGN

Pulse Amplitude Modulation (PAM) is a one dimensional or in other words real modulation. Simply put it is an extension of BPSK with M amplitude levels instead of two. This can be a bit confusing because BPSK can be looked at as a phase modulation and its natural extension must be QPSK or 8-PSK modulations. To remove this ambiguity lets call M-PAM an extension of simple amplitude modulation but with M levels. In the discussion below we consider M=4 but then extend it to the general case of M=2k (k=1,2,3…).

February 16, 2019June 4, 20225G, Antennas, BER Performance, Channel Modeling

Massive MIMO and Antenna Correlation

We calculate the degradation in Bit Error Rate (BER) performance due to antenna correlation at the Mobile Station and the Base Station. Exponential Correlation Model is used in the simulation.

October 14, 2018December 22, 2018Antennas, BER Performance, Fundamentals, LTE

Massive MIMO Fundamentals and Code

Background Just like different frequency bands and time slots can be used to multiplex users, spatial domain can also be exploited to achieve the same result. It is well known that if there are 4 transmit antennas and 4 receive antennas then four simultaneous data streams can be transmitted over the air. This can be scaled up to 8 x 8 or in the extreme case to 128 x 128. When the number of transmit or receive antennas is greater than 100 we typically call it a Massive MIMO scenario and we need specialized signal processing techniques to handle this […]

February 9, 2018October 20, 2018Antennas, BER Performance, Channel Modeling, LTE

Fundamentals of Linear Array Processing – Receive Beamforming

In the previous two posts we discussed the fundamentals of array processing particularly the concept of beamforming (please check out array processing Part-1 and Part-2). Now we build upon these concepts to introduce some linear estimation techniques that are used in array processing. These are particularly suited to a situation where multiple users are spatially distributed in a cell and they need to be separated based upon their angles of arrival. But first let us introduce the linear model; I am sure you have seen this before. x=Hs+w Here, s is the vector of symbols transmitted by M users, H […]

August 24, 2017August 28, 2017BER Performance, Channel Modeling, LTE, WiMAX

BER for BPSK-OFDM in Frequency Selective Channel

As the data rates supported by wireless networks continue to rise the bandwidth requirements also continue to increase (although spectral efficiency has also improved). Remember GSM technology which supported 125 channels of 200KHz each, which was further divided among eight users using TDMA. Move on to LTE where the channel bandwidth could be as high as 20MHz (1.4MHz, 3MHz, 5MHz, 10MHz, 15MHz and 20MHz are standardized). This advancement poses a unique challenge referred to as frequency selective fading. This means that different parts of the signal spectrum would see a different channel (different amplitude and different phase offset). Look at […]

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.

July 6, 2017July 7, 2017BER Performance, Fundamentals

Run Python Code from the Browser

Here is a piece of Python code that calculates Bit Error Rate (BER) of BPSK. The code is a bit slow at the moment, compared to MATLAB implementation, but this is work in progress and further optimizations would be carried out. We would like to point out that the main reason for this slower implementation is that a bit by bit error calculation is done, instead of a vectorial implementation. We already pointed out in our previous post that a “for loop” implemented in Python is not that efficient.

June 23, 2017May 7, 2022BER Performance, Fundamentals

BPSK Bit Error Rate Calculation Using Python

Have you ever thought about how life would be without MATLAB. As it turns out there are free and open source options such as Python. We have so far restricted ourselves to MATLAB in this blog but now we venture out to find out what are the other options. Given below is a most basic Python code that calculates the Bit Error Rate of Binary Phase Shift Keying (BPSK). Compare this to our MATLAB implementation earlier [BPSK BER]. There are various IDEs available for writing your code but I have used Enthought Canopy Editor (32 bit) which is free to […]