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Channel Independent Precoder for OFDM-based Systems over Fading Channels

Jorge Ortin, Paloma Garcia, Fernando Gutierrez, Antonio Valdovinos

TL;DR

This work addresses OFDM transmission over fading channels without transmitter channel state information by introducing a channel-independent precoder based on a Hadamard transform and a time-frequency interleaver to redistribute input symbols across precoded outputs. The receiver employs a clipped Zero Forcing equalizer and a deprecoder, with the clipping threshold $c$ tuned to minimize mean squared error and limit noise power transfer. Theoretical noise analyses show that increasing the precoding block size $N$ reduces the variability of instantaneous noise power across carriers, approaching a Gaussian-like, more uniform distribution, while simulations on ITU Vehicular A channels demonstrate BER gains over uncoded OFDM and OFDM-CDM, especially for $N$ in the 16–512 range. The approach provides time-frequency diversity and broadcast-friendly operation (no transmitter CSI), with a flexible precoder size that need not match the OFDM FFT, making it practically impactful for robust multicarrier systems. Overall, the combination of Hadamard-based precoding, interleaving, and a clipped ZF equalizer yields improved BER and resilience to channel variation in fading environments.

Abstract

In this paper we propose an independent channel precoder for orthogonal frequency division multiplexing (OFDM) systems over fading channels. The design of the precoder is based on the information redistribution of the input modulated symbols amongst the output precoded symbols. The proposed precoder decreases the variance of the instantaneous noise power at the receiver produced by the channel variability. The employment of an interleaver together with a precoding matrix whose size does not depend on the number of data carriers in an OFDM symbol allows different configurations of time-frequency diversity which can be easily adapted to the channel conditions. The precoder is evaluated with a modified Zero Forcing (ZF) equalizer whose maximum gain is constrained by means of a clipping factor. Thus, the clipping factor limits the noise power transfer in the receiver deprecoding block in low SNR conditions.

Channel Independent Precoder for OFDM-based Systems over Fading Channels

TL;DR

This work addresses OFDM transmission over fading channels without transmitter channel state information by introducing a channel-independent precoder based on a Hadamard transform and a time-frequency interleaver to redistribute input symbols across precoded outputs. The receiver employs a clipped Zero Forcing equalizer and a deprecoder, with the clipping threshold tuned to minimize mean squared error and limit noise power transfer. Theoretical noise analyses show that increasing the precoding block size reduces the variability of instantaneous noise power across carriers, approaching a Gaussian-like, more uniform distribution, while simulations on ITU Vehicular A channels demonstrate BER gains over uncoded OFDM and OFDM-CDM, especially for in the 16–512 range. The approach provides time-frequency diversity and broadcast-friendly operation (no transmitter CSI), with a flexible precoder size that need not match the OFDM FFT, making it practically impactful for robust multicarrier systems. Overall, the combination of Hadamard-based precoding, interleaving, and a clipped ZF equalizer yields improved BER and resilience to channel variation in fading environments.

Abstract

In this paper we propose an independent channel precoder for orthogonal frequency division multiplexing (OFDM) systems over fading channels. The design of the precoder is based on the information redistribution of the input modulated symbols amongst the output precoded symbols. The proposed precoder decreases the variance of the instantaneous noise power at the receiver produced by the channel variability. The employment of an interleaver together with a precoding matrix whose size does not depend on the number of data carriers in an OFDM symbol allows different configurations of time-frequency diversity which can be easily adapted to the channel conditions. The precoder is evaluated with a modified Zero Forcing (ZF) equalizer whose maximum gain is constrained by means of a clipping factor. Thus, the clipping factor limits the noise power transfer in the receiver deprecoding block in low SNR conditions.
Paper Structure (6 sections, 24 equations, 7 figures, 1 table)

This paper contains 6 sections, 24 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Precoding System Description
  3. Statistical characterization of the noise at the deprecoder output
  4. Equalizer Design
  5. Simulation Results
  6. Conclusion

Figures (7)

  • Figure 1: System Block Diagram
  • Figure 2: Example of a time-frequency interleaving pattern with a precoded block size of 16 symbols and 8 subcarriers per OFDM symbol. Symbols corresponding to the same precoding block are moved apart 4 subcarriers and 2 OFDM symbols.
  • Figure 3: BER vs. clipping threshold (SNR = 20 dB)
  • Figure 4: BER vs. clipping threshold (SNR = 10 dB)
  • Figure 5: BER comparison for different precoder block sizes assuming optimum clipping threshold
  • ...and 2 more figures