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On Multiple-Input Multiple-Output OFDM with Index Modulation for Next Generation Wireless Networks

Ertugrul Basar

arXiv:1604.07026v1cs.IT

TL;DR

MIMO-OFDM-IM is studied as an alternative to classical MIMO-OFDM for next-generation wireless networks, with open detector design and analysis questions. The paper proposes and analyzes ML, near-ML, MMSE, and OSIC-based MMSE detectors, finding improved error performance and a trade-off among complexity, spectral efficiency, and error performance under realistic conditions.

  • Problem

    Detector design and error-performance analysis for MIMO-OFDM-IM remain open across applications with different complexity and BER constraints.

  • Method

    The paper proposes ML, near-ML, simple MMSE, and OSIC-based sequential MMSE detectors and derives theoretical ABEP results under realistic channel conditions.

  • Results

    Approximately 3 dB better BER performance is reported for MIMO-OFDM-IM than reference V-BLAST-OFDM at BER 10^-5 for M = 8, N = 16, and K = 13.

  • Takeaways & Limitations

    MIMO-OFDM-IM offers a possible 5G candidate with better BER, flexible active-subcarrier design, and compatibility with higher MIMO setups.

Abstract

from arXiv · show

Multiple-input multiple-output orthogonal frequency division multiplexing with index modulation (MIMO-OFDM-IM) is a novel multicarrier transmission technique which has been proposed recently as an alternative to classical MIMO-OFDM. In this scheme, OFDM with index modulation (OFDM-IM) concept is combined with MIMO transmission to take advantage of the benefits of these two techniques. In this paper, we shed light on the implementation and error performance analysis of the MIMO-OFDM-IM scheme for next generation 5G wireless networks. Maximum likelihood (ML), near-ML, simple minimum mean square error (MMSE) and ordered successive interference cancellation (OSIC) based MMSE detectors of MIMO-OFDM-IM are proposed and their theoretical performance is investigated. It has been shown via extensive computer simulations that MIMO-OFDM-IM scheme provides an interesting trade-off between error performance and spectral efficiency as well as it achieves considerably better error performance than classical MIMO-OFDM using different type detectors and under realistic conditions.

I. INTRODUCTION

The paper motivates MIMO-OFDM-IM as a 5G-oriented combination of MIMO and OFDM-IM, then investigates detector designs and error performance under realistic conditions.

  • Motivation: OFDM-IM conveys information through both M-ary data symbols and the indices of active subcarriers.Only a selected subset of subcarriers is active, while the remainder are set to zero.
  • Motivation: Adjusting the number of active subcarriers creates a trade-off between error performance and spectral efficiency.This flexibility also makes OFDM-IM relevant to high-speed and low-power M2M communications.
  • MIMO-OFDM-IM: MIMO-OFDM-IM combines MIMO and OFDM-IM as an alternative to classical MIMO-OFDM for 5G and beyond networks.Each transmit antenna sends its own OFDM-IM frame, which the receiver separates and demodulates.
  • Contributions: The paper addresses the open problem of designing and analyzing detectors with different error-performance and decoding-complexity constraints.It considers ML, near-ML, simple MMSE, and OSIC-based sequential MMSE detection under realistic conditions.
  • Contributions: The study derives theoretical error-performance results and evaluates MIMO-OFDM-IM using realistic LTE channels and channel-estimation errors.The work includes ML ABEP analysis based on pairwise error probability and theoretical analysis for MMSE detection.

II. MIMO-OFDM-IM AT A GLANCE

MIMO-OFDM-IM extends OFDM index modulation across multiple transmit antennas, encoding information in active-subcarrier locations and QAM symbols before transmission through a MIMO-OFDM chain.

  • Transmitter structure: The transmitter splits mT input bits into T groups, processing one group in each transmit-antenna branch.Each branch constructs its own OFDM-IM frame.
  • OFDM-IM mapping: Each subblock selects K active subcarriers from N using p1 index bits, while p2 = K log2(M) bits select M-QAM symbols.The remaining N − K subcarriers are inactive and set to zero.
  • Index selection: Active-index selection uses reference look-up tables for smaller N and K values or combinatorial number theory for larger values.For N = 4 and K = 2, p1 = 2 bits determine the active-subcarrier indices.
  • Transmitter structure: The resulting subblocks are concatenated, interleaved, transformed by IFFT, and appended with a cyclic prefix before transmission.The interleavers distribute subblock elements across uncorrelated channels.
  • Channel model: The transmitted signals simultaneously traverse a frequency-selective Rayleigh fading MIMO channel with T transmit and R receive antennas.The channel taps are modeled as i.i.d. CN(0, 1/L).
  • Receiver processing: After cyclic-prefix removal, FFT, and deinterleaving, received subblocks are separated and represented by per-subcarrier MIMO signal models.The data vectors may contain zero terms because of index selection.
  • Performance measures: The scheme’s spectral efficiency is mT/(NF + Cp) bits/s/Hz, with SNR defined as Eb/N0,T.Here Eb = (NF + Cp)/m joules/bit.

III. ML DETECTION OF MIMO-OFDM-IM

The paper introduces ML and near-ML detectors for MIMO-OFDM-IM, targeting applications where bit-error performance is critical while reducing the complexity of brute-force detection.

  • Detector design: ML and near-ML detectors are proposed for MIMO-OFDM-IM applications where BER is critical.The brute-force ML detector also receives an ABEP derivation based on pairwise error probability.
  • Detector design: The brute-force ML detector serves as a performance benchmark, whereas the near-ML detector is designed to reduce decoding complexity.The near-ML detector’s theoretical performance analysis is described as intractable.

A. Brute-Force ML Detecion of MIMO-OFDM-IM

The brute-force ML detector jointly detects each MIMO-OFDM-IM subblock by searching possible transmitted vectors and supports analytical error-performance derivation. Its main drawback is the joint search across transmit antennas caused by inter-antenna subblock interference.

  • ML detection: The ML detector performs a joint search over all transmit antennas for each subblock because different antennas interfere.The received subblock model uses stacked signals, a block-diagonal channel matrix, an equivalent data vector, and noise.
  • Error analysis: Pairwise error events within different subblocks are identical, so analyzing one subblock suffices to determine overall system performance.The ABEP analysis therefore derives performance from pairwise error probabilities for MIMO-OFDM-IM subblocks.
  • Error analysis: The conditional pairwise error probability is averaged over the channel distribution using the random variable Γ and its moment-generating function.The derivation expresses Γ as a quadratic form before obtaining its moment-generating function.
  • Error analysis: The unconditional pairwise error probability is obtained from the averaged conditional probability, and ABEP follows through an asymptotically tight union upper bound.The analysis also notes closed-form solutions for the relevant integral for different N values.
  • Error analysis: For worst-case events with no active-index errors and one erroneously detected M-ary symbol, the diversity order is evaluated from the resulting pairwise-error expression.Events involving active-index errors improve the distance spectrum because they occur less frequently.

B. Simplified Near-ML Detection of MIMO-OFDM-IM

The near-ML detector reduces the brute-force ML search by computing per-antenna probabilistic measures for reference-table elements. Its complexity has the same order as the classical MIMO-OFDM ML detector while preserving a substantially smaller search space.

  • Complexity: The brute-force ML detector has complexity ∼O(M KT), compared with ∼O(M T) for classical MIMO-OFDM.The near-ML detector is proposed to achieve the same order of decoding complexity as the classical MIMO-OFDM ML detector.
  • Detector operation: The near-ML procedure uses conditional probability calculations based on the received signals and the reference look-up table rather than the full joint ML search.The ML detector maximizes the joint conditional pdf, whereas near-ML evaluates probabilistic measures separately for each transmit antenna.
  • Detector operation: The near-ML detector calculates conditional probability values for reduced per-subcarrier realizations, then combines them into probabilities for each transmit antenna.The search space for each subcarrier is reduced to (M + 1)^T possible realizations.
  • Detector operation: It selects the most likely reference look-up-table element after calculating C_M^K probability values for each transmit antenna.The probabilities transform measurements involving symbols from different antennas into antenna-specific probabilities.
  • Numerical example: For T = M = K = 2 and N = 4, the reference look-up table contains C_M^K = 16 elements, while the reduced vector has (M + 1)^T = 9 realizations.The example requires N(M + 1)^T = 36 probability calculations.

IV. MMSE DETECTION OF MIMO-OFDM-IM SCHEME

The MMSE section addresses the high decoding complexity of brute-force and near-ML detectors by introducing lower-complexity MMSE detection and an approximate ABEP analysis.

  • Motivation: Brute-force and near-ML decoding can remain costly for higher-order modulations and larger MIMO systems.The section motivates MMSE detection as an alternative to exponentially increasing ML-detector complexity.
  • Motivation: The proposed simple MMSE detector significantly reduces decoding complexity relative to ML-based detectors.An approximate ABEP is also provided as a reference for MMSE and LLR detectors.

A. Simple MMSE Detection of MIMO-OFDM-IM

Simple MMSE detection filters each subcarrier observation, reconstructs subblock estimates, and decides among index-modulated candidates using conditional probability. Its analysis provides an upper-bound error approximation under practical assumptions.

  • Detection procedure: Because index information is carried by subblocks, processing the received vector alone cannot directly recover transmitted symbols as in classical MIMO-OFDM.The proposed scheme performs N independent and successive MMSE detections using an MMSE filtering matrix.
  • Detection procedure: MMSE filtering and rearrangement eliminate interference between subblocks from different transmit antennas before subblock decisions are made.The filtered estimates are characterized through conditional means and covariance matrices.
  • Decision rule: The simple MMSE detector chooses the most likely subblock by maximizing its conditional probability density.The decision rule uses the diagonal structure of the covariance matrix after dropping constant terms.
  • Error analysis: The error analysis defines Δ_n as the squared distance between transmitted and erroneously detected symbols and V_n as a ratio of correlated random variables.The distribution of V_n is nonparametric, depends on SNR, and is identical across subcarriers and transmit antennas.
  • Error analysis: Under the approximation N_0,F ≪ 1, the unconditional pairwise error probability is upper-bounded and integrated over the distributions of Z_n.The resulting expression has a closed-form solution in the cited appendix.
  • Performance characterization: For worst-case pairwise events, the simple MMSE detector has diversity order one, and its upper-bound UPEP is independent of transmit-antenna count when T = R.A tighter approximation can instead average over V_n using a semi-analytical approach.

B. MMSE and LLR Detection of MIMO-OFDM-IM

The MMSE-LLR detector provides a low-complexity approach for detecting MIMO-OFDM-IM by estimating active subcarriers and transmitted constellation symbols from LLR values.

  • The MMSE-LLR detector calculates an LLR value for each subcarrier of each transmitter and subblock.
  • For reference look-up tables, active indices are selected using the highest LLR sum among table elements.
  • With combinatorial active-index selection, the detector chooses K subcarriers having the maximum LLR values.
  • The selected active indices determine the index bits, while M-ary symbols are detected on those active subcarriers.
  • The MMSE-LLR detector requires approximately O(M) complex multiplications per subcarrier.

C. MMSE and LLR Detection of MIMO-OFDM-IM with OSIC

The OSIC-MMSE-LLR detector extends MMSE-LLR detection with ordered successive interference cancellation, selecting subblocks by an empirical SINR-related metric before updating received signals.

  • OSIC-MMSE-LLR performs N successive MMSE detections and computes an empirical min-max metric for each subblock.
  • The subblock with the minimum metric is selected as best in terms of signal-to-interference-plus-noise ratio, and subblocks are ordered accordingly.
  • After MMSE estimates are obtained, conditional means and variances support LLR calculation and detection of active indices and M-ary symbols.
  • Estimated signal vectors are used to update the received signal vectors, and the procedure repeats until all OFDM-IM subblocks are demodulated.

V. SIMULATION RESULTS AND COMPARISONS

The simulations compare MIMO-OFDM-IM with classical V-BLAST-OFDM across detectors, configurations, spectral efficiencies, and channel-estimation conditions. MIMO-OFDM-IM generally improves BER and offers adjustable spectral efficiency, while complexity and imperfect channel estimation remain important considerations.

  • Simulation setup: MIMO-OFDM-IM is evaluated against classical V-BLAST-OFDM using theoretical and Monte Carlo results across detectors and system configurations.The study considers ML, near-ML, MMSE-type detectors, multiple MIMO configurations, and realistic channel conditions.
  • Detection complexity: Brute-force ML decoding has complexity ∼O(M KT), whereas the proposed near-ML detector has the same order complexity as classical MIMO-OFDM ML detection.The complexity comparison is expressed in complex multiplications per subcarrier.
  • ML and near-ML detection: MIMO-OFDM-IM provides considerable BER improvement over V-BLAST-OFDM with ML or near-ML detection at matched spectral efficiencies.For N = 4, K = 2, the compared configurations use 1.87 and 3.74 bits/s/Hz, respectively, and both schemes obtain diversity order R.
  • MMSE detection: With QPSK and MMSE-type detectors, simple MMSE and MMSE-LLR perform almost identically for MIMO-OFDM-IM and outperform classical V-BLAST-OFDM using MMSE detection.For N = 4, K = 3, matched spectral efficiencies are 3.74 and 7.48 bits/s/Hz for the 2 × 2 and 4 × 4 configurations.
  • Spectral-efficiency trade-off: Approximately 3 dB better BER is obtained at BER 10^-5 for M = 8, N = 16, K = 13 at the same spectral efficiency as V-BLAST-OFDM.Changing K adjusts spectral efficiency, with BER potentially better or worse than the 11.2 bits/s/Hz reference configuration; 64-QAM degrades BER.
  • Realistic channel conditions: Imperfect channel estimation considerably degrades all schemes, while Alamouti-OFDM is best in the first configuration and MIMO-OFDM-IM is best at the higher spectral efficiency.The comparisons use realistic EPA channel conditions and MMSE-LLR detection.

VI. CONCLUSIONS

The paper concludes that MIMO-OFDM-IM is a candidate for 5G networks because it combines improved BER, flexible active-subcarrier design, and compatibility with higher MIMO setups. It also identifies several topics for future investigation.

  • Overall conclusion: MIMO-OFDM-IM offers a trade-off among complexity, spectral efficiency, and error performance compared with classical MIMO-OFDM.The conclusion presents this trade-off as a central outcome of the study.
  • Contributions: The proposed detector family includes ML, near-ML, simple MMSE, and MMSE-LLR-OSIC methods with theoretical ABEP analysis.These detectors and their performance are examined for MIMO-OFDM-IM.
  • Main features: The main reported features are better BER, flexible adjustment of active OFDM subcarriers, and better compatibility with higher MIMO setups.The active-subcarrier count provides a flexible system-design parameter.
  • Open topics: Diversity methods, generalized OFDM-IM, high-mobility implementation, and transmit-antenna index selection remain open topics for MIMO-OFDM-IM.These areas are explicitly identified for further investigation.
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