Understanding OFDM, CDMA, and Orthogonality

Ever wondered how Wi-Fi, LTE, and 5G send lots of data without signals clashing? This short post explains the difference between OFDM and CDMA, the history of CDMA, GPS applications, and why orthogonality is so important.

---

Narrowband vs Wideband Signals

✅ Narrowband (OFDM)

Think of a highway. Instead of all cars (data) fighting for one lane, OFDM splits the channel into many small lanes called subcarriers. Each subcarrier carries a small portion of the data.

Example: A 20 MHz Wi-Fi channel can be split into 64 subcarriers. Each subcarrier is ~312.5 kHz wide — that’s “narrowband.”

Advantage: Tight packing of subcarriers with low interference when designed using orthogonality.

⚖️ Wideband (CDMA)

CDMA spreads a user’s signal across the entire channel using a unique code. Imagine one car using the whole highway but marked by a special tag so receivers can extract it from the mix.

History & Applications:

The idea of spread spectrum systems dates back to military applications during World War II. The main benefits were to hide a signal, protect it against eavesdropping, and achieve robustness against interference. Correlating a spreading sequence is also used in radar systems to measure propagation delay and derive object positions.

A famous example is the Global Positioning System (GPS), developed around 1970, which uses nearly orthogonal spreading codes to separate signals from different satellites. This was one of the first major applications of CDMA ^[1].

In mobile communications, CDMA became a key multiple access technique in the last 10 years. Qualcomm proposed the first CDMA mobile system in 1988, which became the IS-95 standard (cdmaOne) and later evolved into cdma2000. Another major CDMA-based system is UMTS, used in Europe ^[2].

Advantage: Robustness to interference and multipath, with the ability to separate signals from multiple users using codes.

Quick intuition: OFDM = many narrow lanes (subcarriers). CDMA = one wide lane with coded cars.

The Power of Orthogonality

Orthogonality prevents interference among OFDM subcarriers even when they overlap in frequency.

In math

Two vectors are orthogonal if their dot product is zero. Example:

a = (1, 0),   b = (0, 1)
a ⋅ b = (1×0) + (0×1) = 0

In signals

Two waveforms f1(t) and f2(t) are orthogonal over interval [0,T] if:

∫₀^T f₁(t) · f₂(t) dt = 0

Example — sine & cosine

f₁(t) = sin(2πt),   f₂(t) = cos(2πt)
Over one full period (T = 1):
∫₀¹ sin(2πt) cos(2πt) dt = 0

Example — two different-frequency sines

f₁(t) = sin(2πt),   f₂(t) = sin(4πt)
Over T = 1:
∫₀¹ sin(2πt) sin(4πt) dt = 0

Why Orthogonality Matters

OFDM subcarriers are chosen to be orthogonal over the symbol interval. That means even when their spectra overlap, a receiver using the correct demodulation (FFT) recovers each subcarrier without interference from others. This underpins high-speed systems like Wi-Fi, LTE, and many 5G numerologies.

Visual Context

Illustration: Generator and Discriminator mapping process for OFDM.

Tip: For best results in Blogger, click the image icon in the editor to upload images, then switch to HTML view to ensure the correct src path is in place.

---

✅ That’s all — a short, shareable explanation of OFDM, CDMA, orthogonality, and historical context perfect for a blog post. Thanks for reading!

References:

[1] Schulze, H., & Lüders, C. (2005). Theory and applications of OFDM and CDMA: Wideband wireless communications. John Wiley & Sons.

[2] Nair, A., & Tanwar, S. (2024). Resource allocation in V2X communication: State-of-the-art and research challenges. Physical Communication, 64, 102351.