Link Budget and System Architecture System Design Informational

What is the advantage of using OFDM modulation for wideband communication over a frequency selective channel?

Q: Why not use a single-carrier system with equalization?

A single-carrier system can handle multipath using an adaptive equalizer (Viterbi, MMSE, or decision-feedback equalizer), but the equalizer complexity grows linearly with the channel delay spread: for a 5 us delay spread at 20 MHz bandwidth: the equalizer needs 100 taps, each updated every symbol interval. Training overhead and computational cost are high. OFDM converts this into N one-tap equalizations (trivial). The OFDM advantage increases with bandwidth and delay spread. However: single-carrier with frequency-domain equalization (SC-FDE) is an alternative that achieves similar performance to OFDM with lower PAPR. SC-FDE is used in some military systems and was adopted for LTE uplink as SC-FDMA.

Q: How does OFDM work with MIMO?

OFDM and MIMO are naturally complementary: each OFDM subcarrier is independently and identically processed in the MIMO spatial domain. For a 4×4 MIMO-OFDM system with 1024 subcarriers: each subcarrier has a 4×4 MIMO channel matrix H_k. The MIMO processing (precoding, spatial multiplexing, or diversity combining) is applied per subcarrier. The total processing: 1024 × 4×4 matrix operations per OFDM symbol. This is more efficient than MIMO with a single wideband carrier, which would require equalization across both space and frequency simultaneously. Massive MIMO (64+ antennas) with OFDM: each subcarrier is processed with a 64×N_users beamforming matrix. The large number of antennas provides spatial multiplexing gain and interference suppression.

Q: What is the cyclic prefix overhead?

The CP is pure overhead (it carries redundant information and reduces the net data rate). CP overhead = T_CP / (T_symbol + T_CP). For LTE normal CP: 4.7 us / (66.7 + 4.7) = 6.6%. For LTE extended CP: 16.7 us / (66.7 + 16.7) = 20%. For 5G NR at 30 kHz subcarrier spacing: T_symbol = 33.3 us, T_CP = 2.3 us. Overhead = 6.5%. At 120 kHz (mmWave): T_symbol = 8.33 us, T_CP = 0.57 us. Overhead = 6.4%. The CP overhead is a fundamental cost of OFDM. Reducing the CP below the channel delay spread causes ISI. Increasing the CP beyond the delay spread wastes capacity. The CP length should be matched to the deployment scenario (indoor: short CP, outdoor macro: long CP).

OFDM (Orthogonal Frequency Division Multiplexing) provides a fundamental advantage for wideband communication over frequency-selective channels: it converts a single wideband channel with intersymbol interference (ISI) into many narrowband subchannels that each experience flat fading, eliminating ISI without complex equalization. The mechanism: (1) A wideband channel (e.g., 20 MHz) has a frequency-selective response due to multipath: the channel gain and phase vary across the bandwidth. The delay spread tau_rms causes ISI for symbol rates > 1/tau_rms. For indoor channels: tau_rms ≈ 50-100 ns (ISI-free bandwidth < 2-4 MHz). For outdoor urban: tau_rms ≈ 1-5 us (ISI-free bandwidth < 40-200 kHz). (2) OFDM divides the 20 MHz channel into N subcarriers (e.g., 1024), each with bandwidth 20 MHz/1024 ≈ 20 kHz. Each 20 kHz subcarrier is much narrower than the coherence bandwidth (> 200 kHz), so it experiences flat fading (constant gain and phase across its bandwidth). No ISI within each subcarrier. (3) A cyclic prefix (CP) is added to each OFDM symbol: a copy of the last portion of the symbol prepended to the beginning. The CP length must be > tau_max (maximum excess delay). For tau_max = 5 us and symbol duration 50 us: CP = 5 us (10% overhead). The CP absorbs the multipath, preventing ISI between symbols. (4) Simple equalization: each subcarrier requires only a single complex multiplication (one-tap equalizer) to correct for the channel gain and phase. Compare to a wideband single-carrier system, which would need a 50-100 tap adaptive equalizer for the same channel. Additional advantages: natural integration with MIMO (each subcarrier can be independently processed), efficient spectrum utilization (subcarriers are orthogonal, no guard bands), and flexible resource allocation (assign different subcarriers and modulation to different users).

Category: Link Budget and System Architecture

Updated: April 2026

Product Tie-In: System Components

OFDM for Frequency-Selective Channels

OFDM has become the dominant modulation scheme for wideband wireless communications because of its elegant solution to the multipath challenge and its natural compatibility with MIMO and adaptive resource allocation.

Parameter	Free Space	Urban	Indoor
Path Loss Model	Friis (1/r²)	Okumura-Hata	IEEE 802.11
Fading Margin	0 dB	10-30 dB	5-15 dB
Multipath	None	Severe	Moderate-severe
Typical Range	Line of sight	1-30 km	10-100 m
Shadow Fading (σ)	0 dB	6-12 dB	3-8 dB

Margin Allocation

The mathematical basis of OFDM: an N-point IFFT at the transmitter generates N orthogonal subcarriers. The transmitted signal: x(t) = sum(k=0 to N-1) X_k × e^(j2pi×k×delta_f×t), where X_k is the complex data symbol on subcarrier k and delta_f = 1/T_symbol is the subcarrier spacing. Orthogonality: the subcarriers are spaced by exactly 1/T_symbol, ensuring that each subcarrier has a zero-crossing at the center frequency of every other subcarrier. This allows the subcarriers to overlap in frequency without mutual interference, achieving near-100% spectral efficiency. Cyclic prefix: the CP of length T_CP is prepended to each OFDM symbol. When the channel impulse response is shorter than T_CP: the linear convolution with the channel becomes a circular convolution, and the channel effect on each subcarrier is simply a complex multiplication: Y_k = H_k × X_k + N_k. Equalization is trivial: X_hat_k = Y_k / H_k (one complex division per subcarrier). The channel coefficients H_k are estimated from known pilot symbols (training symbols on specific subcarriers).

Propagation Modeling

LTE: N = 2048 subcarriers (1200 used), delta_f = 15 kHz, symbol duration = 66.7 us, CP = 4.7 us (normal) or 16.7 us (extended). Bandwidth: 20 MHz (maximum). Spectral efficiency: up to 5.5 bps/Hz (64-QAM, rate 5/6, 4×4 MIMO). 5G NR: flexible numerology with delta_f = 15, 30, 60, 120, or 240 kHz. Wider bandwidth: up to 400 MHz (at 120 kHz subcarrier spacing for FR2 mmWave). The wider subcarrier spacing at mmWave provides: longer CP in units of delay spread (mmWave channels have shorter delay spreads due to directional beamforming), and higher tolerance to phase noise (phase noise impact is proportional to 1/delta_f). Wi-Fi 6 (802.11ax): N = 256 (20 MHz), 512 (40 MHz), 1024 (80 MHz), 2048 (160 MHz). delta_f = 78.125 kHz. OFDMA: different subcarriers assigned to different users within the same OFDM symbol. Wi-Fi 7 (802.11be): 4096 subcarriers for 320 MHz bandwidth, 4K-QAM (12 bits per symbol).

Performance verification: confirm specifications against the application requirements before finalizing the design
Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades

Fade Mitigation

(1) Peak-to-average power ratio (PAPR): the sum of N subcarriers can produce high peaks when the subcarrier phases align. PAPR = 10×log10(N) in the worst case (13 dB for 1024 subcarriers). High PAPR requires the power amplifier to operate with large backoff, reducing efficiency. Mitigations: clipping and filtering (1-2 dB loss), tone reservation, selected mapping (SLM), and DFT-spreading (SC-FDMA, used in LTE uplink). (2) Sensitivity to carrier frequency offset (CFO): a frequency offset between the transmitter and receiver oscillators destroys the subcarrier orthogonality, causing inter-carrier interference (ICI). The CFO must be < 1-5% of the subcarrier spacing. For delta_f = 15 kHz: CFO < 150-750 Hz. For mmWave at 28 GHz: this requires oscillator accuracy of 150/28e9 = 5 ppb (achievable with TCXO or PLL). (3) Sensitivity to phase noise: the phase noise of the LO spreads each subcarrier into adjacent subcarriers. The common phase error (CPE) is estimated and corrected from pilot subcarriers. The residual ICI from phase noise limits the achievable modulation order (256-QAM requires LO phase noise < -100 dBc/Hz at 10 kHz offset for 15 kHz subcarrier spacing).

Common Questions

Frequently Asked Questions

Why not use a single-carrier system with equalization?

A single-carrier system can handle multipath using an adaptive equalizer (Viterbi, MMSE, or decision-feedback equalizer), but the equalizer complexity grows linearly with the channel delay spread: for a 5 us delay spread at 20 MHz bandwidth: the equalizer needs 100 taps, each updated every symbol interval. Training overhead and computational cost are high. OFDM converts this into N one-tap equalizations (trivial). The OFDM advantage increases with bandwidth and delay spread. However: single-carrier with frequency-domain equalization (SC-FDE) is an alternative that achieves similar performance to OFDM with lower PAPR. SC-FDE is used in some military systems and was adopted for LTE uplink as SC-FDMA.

How does OFDM work with MIMO?

OFDM and MIMO are naturally complementary: each OFDM subcarrier is independently and identically processed in the MIMO spatial domain. For a 4×4 MIMO-OFDM system with 1024 subcarriers: each subcarrier has a 4×4 MIMO channel matrix H_k. The MIMO processing (precoding, spatial multiplexing, or diversity combining) is applied per subcarrier. The total processing: 1024 × 4×4 matrix operations per OFDM symbol. This is more efficient than MIMO with a single wideband carrier, which would require equalization across both space and frequency simultaneously. Massive MIMO (64+ antennas) with OFDM: each subcarrier is processed with a 64×N_users beamforming matrix. The large number of antennas provides spatial multiplexing gain and interference suppression.

What is the cyclic prefix overhead?

The CP is pure overhead (it carries redundant information and reduces the net data rate). CP overhead = T_CP / (T_symbol + T_CP). For LTE normal CP: 4.7 us / (66.7 + 4.7) = 6.6%. For LTE extended CP: 16.7 us / (66.7 + 16.7) = 20%. For 5G NR at 30 kHz subcarrier spacing: T_symbol = 33.3 us, T_CP = 2.3 us. Overhead = 6.5%. At 120 kHz (mmWave): T_symbol = 8.33 us, T_CP = 0.57 us. Overhead = 6.4%. The CP overhead is a fundamental cost of OFDM. Reducing the CP below the channel delay spread causes ISI. Increasing the CP beyond the delay spread wastes capacity. The CP length should be matched to the deployment scenario (indoor: short CP, outdoor macro: long CP).

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