Cyclic Prefix (CP) in LTE & 5G
- Venkateshu
- Jun 26
- 6 min read
Introduction
Cyclic Prefix (CP) is a crucial component in Orthogonal Frequency Division Multiplexing (OFDM) systems, which are the foundation of LTE and 5G. It serves primarily to combat the detrimental effects of multipath propagation, specifically Inter-Symbol Interference (ISI) and Inter-Carrier Interference (ICI).
Why is Cyclic Prefix Required in LTE/5G?
In wireless communication, signals travel through various paths due to reflections, diffractions, and scattering from objects in the environment. This phenomenon is called multipath propagation. As a result, the receiver receives multiple delayed and attenuated copies of the same transmitted signal.
This multipath propagation leads to two main issues:
Inter-Symbol Interference (ISI): When delayed versions of a previous symbol arrive at the receiver at the same time as the current symbol, they spread into each other, causing distortion and making it difficult for the receiver to correctly decode the data.
Inter-Carrier Interference (ICI): In OFDM, multiple subcarriers are transmitted simultaneously, with their orthogonality ensuring that they don't interfere with each other. However, multipath propagation can cause a loss of this orthogonality, leading to ICI. This means that energy from one subcarrier spills over into adjacent subcarriers, degrading performance.
Source image: https://www.slideserve.com/gavivi/communications-part-ii
The Cyclic Prefix is introduced to address these issues.
How Does Cyclic Prefix Mitigate ISI Issue?
The CP is essentially a copy of the end portion of an OFDM symbol, appended to the beginning of that same symbol.
Here's how it mitigates ISI:
Guard Interval: The CP acts as a "guard interval" between consecutive OFDM symbols. When a new symbol is transmitted, the delayed copies of the previous symbol, due to multipath, can still be arriving at the receiver. As long as the delay spread (the maximum time difference between the first and last arriving multipath components) is shorter than the CP duration, these delayed components of the previous symbol will fall within the CP of the current symbol.
Circular Convolution: By copying the end of the symbol to the beginning, the linear convolution of the transmitted signal with the multipath channel effectively becomes a circular convolution within the useful part of the OFDM symbol (after the CP is removed at the receiver). This is crucial because circular convolution in the time domain corresponds to simple multiplication in the frequency domain. This allows the receiver to use a simple one-tap equalizer for each subcarrier to compensate for the channel effects, greatly simplifying receiver design and making it robust against multipath fading.
Without the CP, the multipath components would cause inter-symbol interference by overlapping with the "useful" part of the subsequent symbol, and the receiver would struggle to distinguish the true symbol.
How Cyclic Prefix Mitigates ICI Issue
While the primary role of the CP is often highlighted for ISI mitigation, it plays an equally critical role in preserving the orthogonality of subcarriers, thereby mitigating ICI.
Here's how:
Maintaining Orthogonality in a Frequency-Selective Channel: In a perfect, ideal channel (e.g., Line of Sight), the subcarriers in OFDM are perfectly orthogonal. This means that at the sampling instant for a given subcarrier, all other subcarriers have zero energy. This orthogonality is achieved by choosing subcarrier frequencies such that they are multiples of Tsym, where Tsym is the useful symbol duration.
Tsym= 1 / subcarrier spacing
However, multipath propagation, which introduces different delays for different frequency components (known as a frequency-selective channel), can destroy this orthogonality. When the channel impulse response (CIR) extends beyond the useful symbol duration, it causes:
Phase Shifts Across Subcarriers: Different delays for different frequency components lead to varying phase shifts across the subcarriers.
Frequency Domain Spreading: This phase distortion in the time domain translates to "smearing" of energy from one subcarrier into its adjacent subcarriers in the frequency domain, leading to ICI.
Converting Linear Convolution to Circular Convolution: This is the key mechanism for ICI mitigation. When the transmitted OFDM symbol (s[n]) passes through a multipath channel (h[n]), the received signal (r[n]) is the linear convolution of the two: r[n]=s[n]∗h[n]. Linear convolution in the time domain corresponds to a complex operation in the frequency domain, making equalization difficult and destroying subcarrier orthogonality.
Preserving Subcarrier Orthogonality: Because the CP transforms the linear convolution into an effective circular convolution (as long as the channel impulse response fits within the CP), the orthogonality of the subcarriers is preserved at the FFT input of the receiver. The frequency-domain response of the channel then appears as a simple multiplicative factor for each subcarrier, without causing energy from one subcarrier to spill into others.
Cyclic Prefix Duration Calculation and its Relationship with Coverage of a Cell
The duration of the Cyclic Prefix is directly related to the maximum expected delay spread in the wireless channel.
CP Duration Calculation:
CP Length for Different Subcarriers
The CP length for different sub-carrier can be calculated using following formula.
and CP time duration can be using following formula.
u is numerology, l is the symbol index here and K is a constant to relate NR basic time unit and LTE basic time unit and can be represented by following equation.
Ts is LTE basic time unit and Tc is NR basic time unit. They are calculated as follows.
The CP duration is chosen to be greater than or equal to the maximum delay spread expected in the cell. If the CP duration is too short, ISI will occur. If it's too long, it reduces spectral efficiency (as it's overhead) and consumes more power.
The values for CP duration are standardized in LTE and 5G. In 5G, multiple numerologies are supported, allowing for flexibility:
Normal Cyclic Prefix: This is the most common CP length.
For 15 kHz SCS (similar to LTE): The OFDM symbol duration (useful part) is approximately 66.67μs. The normal CP is typically around 4.69μs (for most symbols in a slot, with the first symbol having a slightly longer CP of around 5.2μs in some cases).
As SCS increases (e.g., 30 kHz, 60 kHz), the useful symbol duration decreases, and consequently, the normal CP duration also decreases proportionally to maintain a consistent overhead percentage relative to the symbol. For example, for 30 kHz SCS, the CP is around 2.34μs.
Extended Cyclic Prefix: This is a longer CP length, used for specific scenarios with very high delay spread.
In LTE, an extended CP of approximately 16.67μs is available.
In 5G, an extended CP is defined for 60 kHz SCS, with a length of around 4.17μs.
Relation with Coverage of a Cell:
The CP duration has a direct relationship with the coverage of a cell, primarily through its ability to handle delay spread:
Larger Cells = Larger Delay Spread = Longer CP Needed: In larger cells, especially in rural areas or environments with many reflective surfaces, the signal travels longer distances and encounters more obstacles, leading to a wider range of multipath delays. Consequently, the maximum delay spread increases. To effectively mitigate ISI and ICI in such environments, a longer Cyclic Prefix is required.
For example, if a CP can absorb a delay of X microseconds, then the maximum path difference it can tolerate is X×speed of light. For a normal CP of 4.7μs, this corresponds to a path difference of approximately 4.7×10^−6s×3×10^8m/s≈1410 meters (or 1.41 km).
For an extended CP of 16.7μs, it can handle a path difference of about 5 km.
Trade-off: CP Overhead and Spectral Efficiency: While a longer CP is beneficial for combating delay spread in larger cells, it also represents overhead. The CP does not carry useful data, so increasing its duration reduces the overall spectral efficiency of the system. This means that a larger portion of the transmission time is dedicated to the guard interval rather than actual data. Therefore, there's a trade-off: sufficient CP length for channel robustness vs. maximizing data throughput.
Impact on Cell Radius: Mobile network operators choose the appropriate CP length based on the expected channel conditions and cell size.
Normal CP is typically sufficient for most urban and suburban cells, which generally have smaller delay spreads.
Extended CP is reserved for very large cells, often in rural or challenging propagation environments, where the delay spread is significant enough to warrant the increased overhead. The extended CP allows these cells to maintain reliable communication over greater distances.
Summary
Cyclic Prefix is a fundamental enabling technology for OFDM-based systems like LTE and 5G, ensuring robust communication in the presence of multipath. Its duration is carefully chosen to match the expected channel delay spread, directly influencing the cell's ability to cover a certain geographical area while balancing spectral efficiency.
In essence, the CP provides a "buffer" that allows the multipath components to "settle" before the useful part of the symbol is processed. By doing so, it ensures that the received signal within the FFT window at the receiver is a circularly convolved version of the transmitted signal and the channel, thereby maintaining the critical orthogonality of the OFDM subcarriers and preventing ICI.
References:
5. 3GPP TS 38.211: Physical channels and modulation
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