OFDMA

Orthogonal Frequency Division Multiple Access is the multiple access technique that powers 4G LTE downlink and 5G NR, making it one of the most important topics in modern digital communications. OFDMA extends the principle of OFDM by distributing different subcarriers among different users, allowing many users to share the channel simultaneously while maintaining the orthogonality that prevents inter-user interference. Understanding OFDMA requires first understanding why OFDM was needed and then seeing how the multiple access dimension is added.

Core Concept Explanation

OFDM divides the available wideband channel into many narrow subcarriers spaced at Delta_f = 1/Tu apart, where Tu is the useful OFDM symbol duration. This spacing ensures that the sinusoids of all subcarriers are orthogonal to each other — no subcarrier interferes with another. Each subcarrier carries a QAM or PSK symbol and experiences flat fading since its bandwidth is much smaller than the channel coherence bandwidth.

OFDMA takes OFDM and adds a multiple access dimension by assigning different subsets of subcarriers (called resource blocks in LTE) to different users. A resource block in LTE consists of 12 subcarriers times 7 OFDM symbols = 84 resource elements, spanning 180 kHz and 0.5 ms (one slot). The base station scheduler assigns resource blocks to users every Transmission Time Interval (TTI = 1 ms in LTE).

A critical advantage of OFDMA is the ability to exploit multiuser diversity. Different users experience deep fading on different subcarriers at the same time. The scheduler can assign each user the subcarriers where it has good channel conditions, maximizing overall throughput. This is called frequency-selective scheduling and is one reason why LTE achieves much higher spectral efficiency than 3G CDMA.

Mathematical Expression

For an OFDM system with N subcarriers, subcarrier spacing Delta_f, and cyclic prefix duration Tcp, the total symbol duration is:

Ts = Tu + Tcp = N/B + Tcp, where B = N * Delta_f is the total bandwidth.

The orthogonality condition between subcarrier m and n is:

(1/Tu) * integral of exp(j2*pi*m*Delta_f*t) * exp(-j2*pi*n*Delta_f*t) dt = delta(m-n)

This is satisfied when Delta_f = 1/Tu, meaning subcarrier spacing equals the reciprocal of the useful symbol duration.

The spectral efficiency of OFDMA with adaptive modulation is:

SE = (1/(Ts * Delta_f)) * log2(M) bits/s/Hz, where M is the modulation order assigned to each subcarrier.

Practical Understanding

LTE uses OFDMA on the downlink (base to mobile) with 15 kHz subcarrier spacing and cyclic prefix of 4.69 microseconds (normal CP). The number of subcarriers ranges from 72 (1.4 MHz channel) to 1200 (20 MHz channel). The uplink in LTE uses SC-FDMA (Single Carrier FDMA) instead of OFDMA to reduce the peak-to-average power ratio (PAPR), which is a hardware concern for mobile device amplifiers.

5G NR extends OFDMA with flexible numerology: subcarrier spacings of 15, 30, 60, 120, and 240 kHz are supported. Larger subcarrier spacing reduces symbol duration and improves Doppler robustness for high-speed users, while smaller spacing enables larger resource blocks for lower frequency bands.

Given:
Number of subcarriers N = 1200 (20 MHz LTE channel)
Subcarrier spacing Delta_f = 15 kHz
Modulation order M = 64-QAM per subcarrier
Cyclic prefix Tu fraction = 1/14 of symbol time

Why this formula applies:
LTE 20 MHz uses 1200 active subcarriers out of 2048 FFT points.
Spectral efficiency requires accounting for CP overhead.

Formula:
Total occupied BW = N * Delta_f
CP overhead factor = Tu / Ts = 14/15 (normal CP, 1 CP per 14 subcarrier symbols)
Bits per subcarrier per symbol = log2(64) = 6
Raw SE = N * 6 / (N * Delta_f) = 6 / Delta_f bits/s/Hz per symbol period

Substitution:
Total BW occupied = 1200 * 15,000 = 18 MHz
With CP overhead = 6 * (14/15) = 5.6 bits/s/Hz

Calculation:
With 1200 subcarriers across 18 MHz, spectral efficiency = 5.6 bits/s/Hz

Final Answer: Peak SE ≈ 5.6 bits/s/Hz for 64-QAM with normal CP (LTE theoretical)

Exam Tip: LTE downlink uses OFDMA; LTE uplink uses SC-FDMA (also called DFT-spread OFDMA) to reduce PAPR. 5G NR supports variable subcarrier spacing (numerology). Subcarrier spacing = 1/Tu is the orthogonality condition — this formula is directly tested in GATE.

• OFDM: N orthogonal subcarriers, each flat-fading, separated by Delta_f = 1/Tu.
• OFDMA: assigns subsets of subcarriers (resource blocks) to different users per TTI.
• LTE resource block: 12 subcarriers x 7 OFDM symbols = 84 resource elements = 180 kHz x 0.5 ms.
• Cyclic prefix: copy of last Tcp seconds of symbol appended at front, eliminates ISI if Tcp exceeds channel delay spread.
• Multiuser diversity: scheduler assigns subcarriers where user has best channel, boosting aggregate throughput.
• LTE uplink: SC-FDMA (DFT-spread OFDM) reduces PAPR compared to OFDMA.

Quick Revision

• Orthogonality condition: Delta_f = 1/Tu (subcarrier spacing = reciprocal of useful symbol time).
• CP must be longer than channel delay spread to eliminate ISI and ICI.
• LTE subcarrier spacing: 15 kHz; 5G NR: 15/30/60/120/240 kHz (numerology).
• LTE DL: OFDMA; LTE UL: SC-FDMA. GATE frequently tests this distinction.
• Spectral efficiency: SE = log2(M) * (Tu/Ts) bits/s/Hz per subcarrier.
• GATE trap: PAPR is a problem for OFDMA (not SC-FDMA), hence SC-FDMA is used in uplink.
• Multiuser diversity requires channel feedback and frequency-selective scheduling at the base station.