Wireless Communication Techniques: OFDM, Diversity, and Propagation

Posted on Apr 8, 2025 in Electronics

Wireless Communication Techniques

1️⃣ Orthogonal Frequency Division Multiplexing (OFDM)

Definition:
OFDM is a multi-carrier modulation (MCM) technique where the total bandwidth is divided into multiple orthogonal subcarriers to reduce Inter-Symbol Interference (ISI) and enhance data transmission efficiency.

Block Diagram:

Transmitter:

Input Data → Serial-to-Parallel → Modulation (QAM/PSK) → IFFT → Cyclic Prefix Addition → Parallel-to-Serial → Transmission

Receiver:

Received Signal → Serial-to-Parallel → Remove Cyclic Prefix → FFT → Demodulation → Parallel-to-Serial → Output Data

Working:

1. Data Stream Division: The input data is split into smaller parallel streams.
2. Subcarrier Modulation: Each stream is modulated using QPSK/QAM.
3. IFFT Processing: Converts frequency domain data into time domain.
4. Cyclic Prefix Addition: Prevents ISI by appending a repeated part of the signal.
5. Transmission & Reception: The signal is sent and later recovered using the reverse process.

✅ Applications of OFDM:

• Used in Wi-Fi (IEEE 802.11a/g/n/ac/ax), 4G LTE, DVB-T, DSL.
• Reduces ISI and multipath fading in wireless networks.
• Supports high-speed broadband data transmission.

2️⃣ Outage Probability of BPSK in Flat Fading Channels

Outage Probability Definition:

P_out =

where γ is the instantaneous SNR, and γ_th is the minimum required SNR.

For Rayleigh fading, the probability follows an exponential distribution:

P_out =

where the average received SNR.

✅ Relation to Fade Margin:
The fade margin is the additional power required to reduce outage probability.

3️⃣ Peak-to-Average Power-Ratio (PAPR) in OFDM

Definition:

PAPR =

Higher PAPR affects power efficiency in amplifiers.

Methods to Reduce PAPR:

1. Clipping & Filtering – Limits peak power but introduces distortion.
2. Coding Techniques – Reduces peaks using special error correction codes.
3. Tone Reservation & Peak Cancellation – Lowers peaks using complementary signals.

📌 Module 4: Diversity, Equalization & Multiple Access

Zero-Forcing (ZF) Equalizer Operation

Definition:
A ZF Equalizer removes ISI by inverting the channel frequency response.

Block Diagram:

Received Signal → ZF Equalizer (H⁻¹ applied) → Output Signal

Mathematical Model:

where H is the channel matrix.

✅ Disadvantage:

Amplifies noise when the channel has low SNR

TDMA, FDMA, and CDMA Comparison

✅ Example Usage:

• TDMA – GSM, 2G
• FDMA – AMPS (Analog Mobile Phone System)
• CDMA – 3G, 4G

Selection Combining Diversity Technique

The receiver selects the best signal out of multiple received signals from different antennas.

Used to combat multipath fading.

✅ Advantages:

• Simple Implementation.
• Low power consumption.

✅ Disadvantages:

Does not fully use diversity gain.

Least Mean Squares (LMS) Algorithm in Adaptive Equalization

Steps in LMS Algorithm:

1. Initialize weights w(n).
2. Compute error: e(n) = d(n) – y(n)
3. Update weights: w(n+1) = w(n) + μe(n)x(n) where μ is the step size.
4. Repeat for each sample.

✅ Application: Used in adaptive equalization.

📌 Module 5: Radio Wave Propagation

Maximum Usable Frequency (MUF) Definition

Maximum Usable Frequency (MUF):

MUF =

where θ is the angle of incidence.

✅ Critical Frequency Expression:

f_c =

where N_max is the max electron density.

✅ Skip Distance Formula:

d_s =

Virtual Height and Skip Distance in Ionospheric Propagation

Virtual Height (h’)

Definition:

Virtual height is the apparent height from which a radio wave appears to be reflected in the ionosphere if the reflection were sharp, rather than gradually bending due to refraction.

📌 Why does this happen?

• In reality, radio waves do not reflect sharply from the ionosphere; instead, they gradually bend due to the variation in electron density.
• However, for practical calculations, we assume that the wave is reflected from a certain height, called the virtual height (h’).

Formula for Virtual Height:

h’ =

where:

• c = Speed of light (3 × 10⁸ m/s)
• T = Total time taken for the wave to travel to the ionosphere and return

The actual path is curved, but it appears as if the wave is reflected from a single point in the ionosphere at height h’.

✅ Significance of Virtual Height:

• Used in designing long-distance HF (High Frequency) communication systems.
• Helps in calculating the angle of incidence required for wave propagation.

Skip Distance (d_s)

Definition:

Skip distance is the minimum distance from the transmitter at which a skywave will return to Earth after ionospheric reflection.

No skywave is received before this distance, creating a skip zone (or dead zone).

Skip distance depends on ionospheric conditions and operating frequency.

Formula for Skip Distance:

d_s =

where:

• h’ = Virtual Height of the ionosphere
• θ = Angle of incidence of the radio wave

Numerical Example:

📌 Given Data:

• Virtual height h’ = 300 km
• Angle of incidence θ =

📌 Calculation:

d_s =

✅ Skip distance = 1040 km.

Critical Frequency & Maximum Usable Frequency (MUF)

Critical Frequency (f_c)

Definition:

The highest frequency that gets reflected back to Earth when sent vertically (90° incidence).

Above this frequency, waves escape into space.

Formula for Critical Frequency:

f_c =

where

= maximum electron density (electrons/m³).

✅ Typical values: 3 – 10 MHz for F-layer.

📌 Explanation:

If the operating frequency is below f_c, the wave is reflected back.

If the operating frequency is above f_c, the wave penetrates into space instead of reflecting.

Maximum Usable Frequency (MUF)

Definition:

MUF is the highest frequency at which a radio wave can still be reflected back to Earth for a given angle of incidence.

Formula for MUF:

MUF =

where:

• f_c = Critical frequency (maximum reflection frequency at normal incidence)
• θ = Angle of incidence