OFDM Transmission in Practical LTE and 5G Systems

Understanding the difference between baseband processing and real RF transmission in modern communication systems.

1. What We Study vs What Is Actually Transmitted

In textbooks, the OFDM signal is written as:

\[ x(t) = \sum_{k} X[k] e^{j 2\pi f_k t} \]

This represents a complex baseband signal. However, antennas cannot transmit complex numbers. They transmit real RF signals.

2. Practical Transmitter Chain (LTE / 5G)

In systems like LTE (4G) and 5G NR, the transmission process works as follows:

Step 1: Digital Baseband Processing

1. Bits
2. QAM Mapping
3. OFDM IFFT
4. Add Cyclic Prefix

The result is:

\[ x_{BB}[n] = I[n] + jQ[n] \]

This is a complex baseband discrete-time signal. It is still digital and complex.

Step 2: Digital-to-Analog Conversion (DAC)

• I[n] → DAC → analog I(t)
• Q[n] → DAC → analog Q(t)

Now we have two real analog signals: In-phase (I) and Quadrature (Q).

Step 3: Upconversion to RF

The signals are mixed with a carrier frequency:

\[ s(t) = I(t)\cos(2\pi f_c t) - Q(t)\sin(2\pi f_c t) \]

This produces a real RF passband signal centered at carrier frequency \( f_c \).

Example carrier frequencies:

• LTE: ~2.1 GHz
• 5G: 3.5 GHz or 28 GHz

This RF signal is sent to the power amplifier and antenna.

3. Are We Using Baseband or Not?

• ✔ Processing is done in baseband
• ✔ Transmission is done in passband (RF)

Baseband exists inside the DSP/FPGA/modem. Passband exists at the RF front-end and antenna.

4. Why We Study Baseband OFDM

The real transmitted RF signal can be written as:

\[ \text{Passband signal} = \Re \{ x_{BB}(t) e^{j2\pi f_c t} \} \]

It is mathematically easier to analyze communication systems in baseband. Channel estimation, equalization, and OTFS processing are all done using complex baseband representation.

5. Receiver Operation

1. Antenna receives RF signal
2. Downconvert using cosine and sine carriers
3. Low-pass filter
4. ADC (Analog-to-Digital Conversion)
5. Recover complex baseband
6. Remove Cyclic Prefix
7. FFT
8. Demodulate

Internally, LTE and 5G always process complex baseband signals.

6. System Flow Summary

Bits
 ↓
QAM
 ↓
IFFT (OFDM)
 ↓
Complex Baseband (I + jQ)
 ↓
DAC
 ↓
I/Q Mixer (Upconversion)
 ↓
Real RF Signal
 ↓
Antenna
        

7. Important Insight

When you simulate OFDM in MATLAB using:

ifft()

You are generating complex baseband samples — exactly what LTE and 5G generate internally before RF upconversion.

What simulations typically omit are:

• DAC
• RF Mixer
• Power Amplifier
• Physical RF Channel

8. Connection to OTFS

OTFS also works in complex baseband and produces complex samples. The RF hardware chain remains the same as OFDM.

The difference lies only in baseband signal processing.