Skip to main content
Home Wireless Communication Modulation MATLAB Beamforming Project Ideas MIMO Computer Networks Lab 🚀

RMS Delay Spread, Excess Delay Spread and Multi-path ...


RMS Delay Spread, Excess Delay Spread, and Multipath (MPCs)

The fundamental distinction between wireless and wired connections is that in wireless connections signal reaches at receiver thru multipath signal propagation rather than directed transmission like co-axial cable. Wireless Communication has no set communication path between the transmitter and the receiver. The line of sight path, also known as the LOS path, is the shortest and most direct communication link between TX and RX. The other communication pathways are called non-line of sight (NLOS) paths. Reflection and refraction of transmitted signals with building walls, foliage, and other objects create NLOS paths. [ Read More about LOS and NLOS Paths]


Multipath Components or MPCs:

The linear nature of the multipath component signals is evident. This signifies that one multipath component signal is a scalar multiple of another.

Let me give you an example to help you understand. Let's assume we're sending an impulse signal from the transmitter. The single impulse response is transmitted to the receiver via LOS and NLOS pathways. The signal is only transmitted via NLOS paths if a LOS path is unavailable. The probability of LOS Communication decreases as the density of the region increases. Because there are numerous obstacles between the transmitter and the receiver, such as buildings, etc.   


Excess Delay Spread:

Excess delay spread is the arrival time difference between the first and final multipath components (MPCs) at the receiver side. For example, suppose the first multipath component arrives at the receiver at time t1, and the last multipath component arrives at time t2. The Excess Delay Spread will then be (t2 -t1).


Power Delay Profile:

The Power Delay Profile shows how received power changes with time dispersion or time delay caused by multipath in a wireless communication channel.

In the above equation, Ac denotes the multipath intensity profile. Ï„ denotes time delay, Î¼Tm denotes average delay spread. 

You can also think of Ac as a power profile that exponentially decreases over time as a multipath delay in time. 


RMS Delay Spread:

The RMS Delay Spread is the power delay profile's second central momentum. We all know that we get multipath components at the receiver end of the wireless communication process. As a result, to obtain the necessary data, we must use stronger multipath and then add them.   Then we divide the total value by the total weights. In the case of the power delay profile computation, power decreases exponentially with time.



Here, in the above equation, σTm denotes rms delay spread. It shows how the RMS delay spread relates to the average delay spread. Apart from the average delay spread, we take the square root value of the square of the difference between the average delay spread and the instantaneous delay spread of the multipath component. [Get MATLAB Code for RMS Delay Spread]
















Why is there significant multipath in the case of very high frequencies?

The signal traversal path is shorter at higher frequencies than at lower frequencies. As a result, cellular network coverage is limited in those situations. And there is little of a LOS component in a city or urban scenario. There are NLOS communication pathways available. When the frequency is very high. However, only a few more robust NLOS components reach the receiver. The rest of the NLOS components are lost in a congested metropolitan area due to repeated reflection and diffraction. Because path loss is directly proportional to the carrier frequency of the operational signal, higher frequencies experience more path loss.


Why RMS Delay Spread is essential for wireless Communication:

In today's wireless Communication, RMS delay spread is a critical characteristic. It depends on an area's physical constructions, like buildings, foliage, etc. There will be linear multipath components, or MPCs, whenever we transmit a signal in a wireless setting. We will receive many copies of the same single-sent impulse response. As a result, it takes some time for all MPCs of the transmitted impulse response to reach the receiver. If we broadcast the following signal immediately after the first, the MPCs of the first symbol cause interference on the receiving side. Because the receiver receives the next symbol and the MPCs of the first symbol. Inter-symbol interferences, or ISI, are the result of this. We broadcast signals at intervals ten times greater than the RMS delay spread to eliminate interference.


Why the Power Delay profile is essential:

The Power Delay Profile shows how received power varies with the time dispersion of MPCs. Only a few MPCs contain practically all abilities for high frequency. Only a few MPCs often carry nearly 80-85% of total energy for higher frequencies.


Now, we are continuously moving to higher frequency bands. You know these bands experience more reflection, scattering, etc. That results in more multipath. And multipath causes fading. And the type of fading tells us whether it is flat fading or frequency selective fading. Different multipaths reaches the receiver at different time. Higher frequency bands experience more Doppler spread as compared to lower frequency bands. You know 5G wireless technology is operating at millimeter wave band, so the Doppler effect will be huge. So, currently, researchers are focusing on the delay-doppler domain to mitigate the effect of Doppler delay spread.


MATLAB Code for calculating different types of delay spread

 

Output

Mean Delay Spread: 1.96 ns
RMS Delay Spread: 1.43 ns
Maximum Excess Delay: 4.00 ns


Also Read: 

 [1] Read more about RMS Delay Spread

[2] More about Channel Input Response (CIR)

[3] Difference between AWGN and Rayleigh Fading

[4] Saleh Valenzuela Channel Model for high frequencies communication

[5]  Impact of Rayleigh Fading and AWGN on Digital Communication Systems

People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

profile

  Website: www.salimwireless.com
  Interests: Signal Processing, Telecommunication, 5G Technology, Present & Future Wireless Technologies, Digital Signal Processing, Computer Networks, Millimeter Wave Band Channel, Web Development
  Seeking an opportunity in the Teaching or Electronics & Telecommunication domains.
  Possess M.Tech in Electronic Communication Systems.


Contact Us

Name

Email *

Message *

Popular Posts

BER vs SNR for ASK, FSK, and PSK

  BER vs. SNR denotes how many bits in error are received in a communication process for a particular Signal-to-noise (SNR) ratio. In most cases, SNR is measured in decibel (dB). For a typical communication system, a signal is often affected by two types of noises 1. Additive White Gaussian Noise (AWGN) 2. Rayleigh Fading In the case of additive white Gaussian noise (AWGN), random magnitude is added to the transmitted signal. On the other hand, Rayleigh fading (due to multipath) attenuates the different frequency components of a signal differently. A good signal-to-noise ratio tries to mitigate the effect of noise.  Calculate BER for Binary ASK Modulation The theoretical BER for binary ASK (BASK) in an AWGN channel is given by: BER  = (1/2) * erfc(0.5 * sqrt(SNR_ask));   Enter SNR (dB): Calculate BER BER vs. SNR curves for ASK, FSK, and PSK Calculate BER for Binary FSK Modulation The theoretical BER for binary FSK (BFSK) in an AWGN channel is g

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... 1. What is Bit Error Rate (BER)? The abbreviation BER stands for bit error rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. It is defined as,  In mathematics, BER = (number of bits received in error / total number of transmitted bits)  On the other hand, SNR refers to the signal-to-noise power ratio. For ease of calculation, we commonly convert it to dB or decibels.   2. What is Signal the signal-to-noise ratio (SNR)? SNR = signal power/noise power (SNR is a ratio of signal power to noise power) SNR (in dB) = 10*log(signal power / noise power) [base 10] For instance, the SNR for a given communication system is 3dB. So, SNR (in ratio) = 10^{SNR (in dB) / 10} = 2 Therefore, in this instance, the signal power i

Difference between AWGN and Rayleigh Fading

Wireless Signal Processing Gaussian and Rayleigh Distribution Difference between AWGN and Rayleigh Fading 1. Introduction Rayleigh fading coefficients and AWGN, or additive white gaussian noise [↗] , are two distinct factors that affect a wireless communication channel. In mathematics, we can express it in that way.  Let's explore wireless communication under two common noise scenarios: AWGN (Additive White Gaussian Noise) and Rayleigh fading. y = hx + n ... (i) The transmitted signal  x  is multiplied by the channel coefficient or channel impulse response (h)  in the equation above, and the symbol  "n"  stands for the white Gaussian noise that is added to the signal through any type of channel (here, it is a wireless channel or wireless medium). Due to multi-paths the channel impulse response (h) changes. And multi-paths cause Rayleigh fading. 2. Additive White Gaussian Noise (AWGN) The mathematical effect involves adding Gauss

FFT Magnitude and Phase Spectrum using MATLAB

  MATLAB Code  % Developed by SalimWireless.Com clc; clear; close all; % Configuration parameters fs = 10000; % Sampling rate (Hz) t = 0:1/fs:1-1/fs; % Time vector creation % Signal definition x = sin(2 * pi * 100 * t) + cos(2 * pi * 1000 * t); % Calculate the Fourier Transform y = fft(x); z = fftshift(y); % Create frequency vector ly = length(y); f = (-ly/2:ly/2-1) / ly * fs; % Calculate phase while avoiding numerical precision issues tol = 1e-6; % Tolerance threshold for zeroing small values z(abs(z) < tol) = 0; phase = angle(z); % Plot the original Signal figure; subplot(3, 1, 1); plot(t, x, 'b'); xlabel('Time (s)'); ylabel('|y|'); title('Original Messge Signal'); grid on; % Plot the magnitude of the Fourier Transform subplot(3, 1, 2); stem(f, abs(z), 'b'); xlabel('Frequency (Hz)'); ylabel('|y|'); title('Magnitude of the Fourier Transform'); grid on; % Plot the phase of the Fourier Transform subplot(3, 1, 3); stem(f,

Constellation Diagrams of ASK, PSK, and FSK

Modulation ASK, FSK & PSK Constellation BASK (Binary ASK) Modulation: Transmits one of two signals: 0 or -√Eb, where Eb​ is the energy per bit. These signals represent binary 0 and 1.  BFSK (Binary FSK) Modulation: Transmits one of two signals: +√Eb​ ( On the y-axis, the phase shift of 90 degrees with respect to the x-axis, which is also termed phase offset ) or √Eb (on x-axis), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  BPSK (Binary PSK) Modulation: Transmits one of two signals: +√Eb​ or -√Eb (they differ by 180 degree phase shift), where Eb​ is the energy per bit. These signals represent binary 0 and 1.  This article will primarily discuss constellation diagrams, as well as what constellation diagrams tell us and the significance of constellation diagrams. Constellation diagrams can often demonstrate how the amplitude and phase of signals or symbols differ. These two characteristics lessen the interference between t

BER performance of QPSK with BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc

   Compare the BER performance of QPSK with other modulation schemes (e.g.,  BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc) under similar conditions. MATLAB Code clear all; close all; % Set parameters for QAM snr_dB = -20:2:20; % SNR values in dB qam_orders = [4, 16, 64, 256]; % QAM modulation orders % Loop through each QAM order and calculate theoretical BER figure; for qam_order = qam_orders     % Calculate theoretical BER using berawgn for QAM     ber_qam = berawgn(snr_dB, 'qam', qam_order);     % Plot the results for QAM     semilogy(snr_dB, ber_qam, 'o-', 'DisplayName', sprintf('%d-QAM', qam_order));     hold on; end % Set parameters for QPSK EbNoVec_qpsk = (-20:20)'; % Eb/No range for QPSK SNRlin_qpsk = 10.^(EbNoVec_qpsk/10); % SNR linear values for QPSK % Calculate the theoretical BER for QPSK using the provided formula ber_qpsk_theo = 2*qfunc(sqrt(2*SNRlin_qpsk)); % Plot the results for QPSK semilogy(EbNoVec_qpsk, ber_qpsk_theo, 's-', &#

Channel Impulse Response (CIR)

Channel Impulse Response (CIR) Wireless Signal Processing CIR, Doppler Shift & Gaussian Random Variable  The Channel Impulse Response (CIR) is a concept primarily used in the field of telecommunications and signal processing. It provides information about how a communication channel responds to an impulse signal.   What is the Channel Impulse Response (CIR) ? It describes the behavior of a communication channel in response to an impulse signal. In signal processing,  an impulse signal has zero amplitude at all other times and amplitude  ∞ at time 0 for the signal. Using a Dirac Delta function, we can approximate this.  ...(i) δ( t) now has a very intriguing characteristic. The answer is 1 when the Fourier Transform of  δ( t) is calculated. As a result, all frequencies are responded to equally by  δ (t). This is crucial since we never know which frequencies a system will affect when examining an unidentified one. Since it can test the system for all freq