Derivation of expression for a Gaussian Filter with 3 dB bandwidth

In GMSK modulation (used in GSM and DECT standard), a GMSK signal is generated by shaping the information bits in NRZ format through a Gaussian Filter. The filtered pulses are then frequency modulated to yield the GMSK signal. GMSK modulation is quite insensitive to non-linearities of power amplifier and is robust to fading effects. But … Read more

Sampling Theorem – Bandpass or Intermediate or Under Sampling

Prerequisite: Sampling theorem – baseband sampling Intermediate Sampling or Under-Sampling A signal is a bandpass signal if we can fit all its frequency content inside a bandwidth . Bandwidth is simply the difference between the lowest and the highest frequency present in the signal. “In order for a faithful reproduction and reconstruction of a bandpass … Read more

Sampling Theorem – Baseband Sampling

For Matlab demo of sampling see here. “Nyquist-Shannon Sampling Theorem” is the fundamental base over which all the digital processing techniques are built. Processing a signal in digital domain gives several advantages (like immunity to temperature drift, accuracy, predictability, ease of design, ease of implementation etc..,) over analog domain processing. Analog to Digital conversion: In … Read more

OFDM simulation – performance in AWGN channel

Goal: Simulate discrete-time cyclic-prefixed OFDM communication system. Explain role of IFFT/FFT, cyclic prefix. Simulate M-QPSK / M-QAM based cyclic prefixed OFDM over AWGN channel. Discrete-time implementation of baseband CP-OFDM The schematic diagram of a simplified cyclic-prefixed OFDM (CP-OFDM) data transmission system is shown in Figure 1. The basic parameter to describe an OFDM system is … Read more

Introduction to OFDM – orthogonal Frequency division multiplexing – part 4 – Cyclic Prefix

Consider a non-ideal channel h(t)≠δ(t), that causes delay dispersion. Delay dispersion manifests itself as Inter Symbol Interference (ISI)on each subcarrier channel due to pulse overlapping. It will also cause ICC (Inter Carrier Interference ) due to the non-orthogonality of the received signal. Adding cyclic prefix to each OFDM symbol mitigates the problems of ISI and … Read more

Introduction to OFDM – orthogonal Frequency division multiplexing – part 3

In the previous article, the architecture of an OFDM transmitter was described using sinusoidal components. Generally, an OFDM signal can be represented as \(s(t)\) = symbols mapped to chosen constellation (BPSK/QPSK/QAM etc..,) \(f_n\) = orthogonal frequency This equation can be thought of as an IFFT process ( Inverse Fast Fourier Transform). The Fourier transform breaks a … Read more

Introduction to OFDM – orthogonal Frequency division multiplexing – part 2

Article moved to new pages The article has been consolidated into these following pages. Please refer these links. If you are looking for Matlab code refer this ebook : Simulation of Digital Communication Systems by Mathuranathan Viswanathan (1) Introduction to OFDM – Orthogonal Frequency Division Multiplexing (2) An OFDM Communication System – Implementation Details (3) … Read more

Introduction to OFDM – orthogonal Frequency division multiplexing

In modulations, information is mapped on to changes in frequency, phase or amplitude (or a combination of them) of a carrier signal. Multiplexing deals with allocation/accommodation of users in a given bandwidth (i.e. it deals with allocation of available resource).OFDM is a combination of modulation and multiplexing. In this technique, the given resource (bandwidth) is … Read more

Eb/N0 Vs BER for BPSK over Rayleigh Channel and AWGN Channel

The phenomenon of Rayleigh Flat fading and its simulation using Clarke’s model and Young’s model were discussed in the previous posts. The performance (Eb/N0 Vs BER) of BPSK modulation (with coherent detection) over Rayleigh Fading channel and its comparison over AWGN channel is discussed in this post. We first investigate the non-coherent detection of BPSK … Read more

Simulation of Rayleigh Fading ( Clarke’s Model – sum of sinusoids method)

A multipath fading channel  can be modeled as a FIR (Finite Impulse Response) filter with the following impulse response. $$ h( \tau ; t ) = h_{0}(t) \delta ( \tau – \tau_{0}(t)) + h_{1}(t) \delta ( \tau – \tau_{1}(t)) + . . . + h_{L-1}(t) \delta ( \tau – \tau_{L-1}(t)) $$ where h(τ,t) is the … Read more