AWGN – 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).

June 17, 2020June 3, 2022Fundamentals

Frequency Estimation Using Zero Crossing Method

In this post we present the simplest method of frequency estimation that is called the Zero Crossing (ZC) method. Since a sine wave crosses the x-axis twice during each cycle, we can simply count the number of crossings and divide it by two and again divide it by the observation window size, giving us the frequency in Hertz.

February 2, 2020June 3, 2022BER Performance, Modulation

MSK Demodulation Using a Discriminator

It is widely believed that performance of non-coherent receivers is much worse than performance of coherent receivers in terms of Bit Error Rate (BER). Although this is true to some extent but as we show in this post the difference in performance is not that much in case of Minimum Shift Keying (MSK). In fact, there is only a difference of about one dB in an AWGN environment at high Signal to Noise Ratios (SNR). The difference is somewhat larger in flat fading environment but given the simplicity of implementation of a non-coherent receiver the trade-off might be worth it.

January 13, 2020January 19, 2025BER Performance, Modulation

Orthogonal Minimum Shift Keying (OMSK)

In this post we consider a special case of MSK called Orthogonal MSK (OMSK) where the power of both the signals is the same (or almost the same) and there is no frequency offset. However, there is a phase offset of 90 degrees. As is evident from our previous posts MSK can be viewed as BPSK with information being transferred via in-phase (I) and quadrature (Q) carriers alternatively. In OMSK the interferer is 90 degrees offset from the signal of interest. So, when there is information being transmitted via I, interferer is on Q and when information is being transmitted via Q, interferer is on I.

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.

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…).

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.

October 30, 2014December 10, 2014Fundamentals

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 […]