The choice of 15 kHz subcarrier spacing in 4G LTE is a result of balancing multiple technical considerations and practical implementation factors. Let’s delve into the main reasons behind this decision:

## Use of 15 kHz Subcarrier Spacing in LTE.

### A. Channel Characteristics and Coherence Bandwidth.

**Flat Fading Channel:**

Each subcarrier in LTE has a bandwidth of 15 kHz, which is smaller than the typical coherence bandwidth of 200-300 kHz. This means each subcarrier experiences flat fading, where the channel characteristics remain constant over the subcarrier bandwidth.

This simplifies equalization at the receiver, making it easier to handle the fading and environmental effects that affect the signal.

### B. Compatibility with Multi-Technology Handsets.

**Unified Clock Timing:**

Different technologies such as GSM, UMTS, and LTE can share the same clock timing, simplifying the design of multi-technology handsets.

In LTE, for a bandwidth (BW) of 10 MHz, there are 600 subcarriers. For efficient FFT/IFFT processing, the number of points (N_{fft}) should be a power of 2, with the next power of two being 1024.

### C. Practical Implementation.

**Sampling Frequency (Fs):**

**Calculation:** Fs = Nfft * Δf (where Δf is the subcarrier spacing).

For BW = 10 MHz, Fs = 1024 * 15 kHz = 15.36 MHz.

This sampling frequency is an integer multiple of the 3.84 MHz chip rate used in UMTS (Fs = 4 * 3.84 MHz), facilitating integration with existing systems.

### 4. Optimal Subcarrier Spacing Selection.

**Symbol Timing and FFT Efficiency:**

**Subcarrier Spacing Options:**While subcarrier spacing such as 7.5 kHz, 30 kHz, or 60 kHz could also be used, 15 kHz was chosen due to its optimal balance in multi-carrier transmission.**Lower Subcarrier Spacing:**Smaller spacing (e.g., 7.5 kHz) would lead to higher susceptibility to frequency errors, especially due to Doppler effects in mobile environments.**Higher Subcarrier Spacing:**Larger spacing (e.g., 30 kHz or 60 kHz) would reduce the length of the OFDM symbol, complicating the insertion of a cyclic prefix (CP) necessary to combat inter-symbol interference (ISI).

**Doppler Effect and Frequency Error:**

**Smaller Subcarrier Spacing:**Higher percentage of frequency error due to Doppler shifts, adversely affecting signal quality.**Larger Subcarrier Spacing:**Shorter symbol length (λ = c/f), making it difficult to insert a sufficiently long CP to protect against ISI.

### Summary

The 15 kHz subcarrier spacing in LTE was chosen as an optimal value that balances the trade-offs between handling flat fading channels, maintaining compatibility with other technologies, ensuring efficient FFT processing, and minimizing the impact of Doppler shifts. This decision supports the robust and efficient performance of LTE, making it well-suited for the diverse and demanding requirements of modern mobile communication.

Read Also: What is LTE Frame Structure?