Isometric Data Sequences and Data-Modulation Schemes in Fading Channels

Abstract

In multiplicative fading channels, joint channel estimation and data detection (CE/DD) schemes cannot differentiate among certain sequences of amplitude-and/or phase-modulated (AM/PM) symbols drawn from rotationally invariant signal constellations. This paper identifies these so-called isometric sequences as the main source of performance degradation, and introduces a unifying framework that effectively solves the problem by using asymmetric signal constellations (ASC) and a normalized innovations-based detector. The encompassing nature of the solution is clearly demonstrated by showing that seemingly unrelated previous results, such as training-based solutions, can be viewed as special cases of the modulation-based solution discussed here. A comprehensive analysis, supported by simulation studies, of the relationships among modulation schemes, isometry, and detection performance is provided. Results indicate that the proposed ASC solution offers excellent performance without incurring significant complexity or reducing the transmission rate. Furthermore, it is shown to be robust in various fading rates, and for different signal constellations.

Superimposed asymmetric modulation in narrowband fading channels using orthogonal codes

“…Note that the KF for TDM PAT in [5] relies solely on the first-order Gauss-Markov hypermodel to updateĥ k|k and P k|k at non-pilot points (Hypermodel TDM PAT). This is different from the KF in [4] where it operates in decision-directed mode for every symbol in the frame (Decision-directed TDM PAT). Nonetheless, a Hypermodel TDM ASC scheme could similarly be set up by replacing the pilot symbol time slots in Hypermodel TDM PAT with ASCs and by using the receiver model in [5].…”

“…Joint channel estimation / data detection (CE/DD) systems suffer from irreducible error floors as a result of the combined effects of erroneous data detection and large estimation errors [1]. It was shown in [4] that the cause is isometry, which can be defined as ambiguity in detecting the correct data symbol that arises from multiplicative channel fading effects and rotational invariance of PSK constellations. One solution to this problem is time-divisionmultiplexed (TDM) pilot-assisted transmission (PAT) in which detection ambiguity is eliminated at the receiver.…”

“…As KF is a recursive estimator, the channel initial conditions need to be known. In the absence of prior information, the channel estimateĥ 0|0 = 0 and the estimation covariance P 0|0 = 1 are used to match the statistical conditions of a Rayleigh fading channel [2], [4]. The ML detector selects the data sequence {d k } based on the criterion in Table I and derived in Appendix I.…”

“…Recently, a method that involves the periodic TDM of asymmetric signal constellations (ASC) was proposed in [4] to break isometry using a decision-directed KF/ML joint CE/DD. Under this receiver model, TDM ASC achieves similar mean square error (MSE) and bit error rate (BER) performance as TDM PAT [4]. Hence, this method has the potential to replace TDM PAT because it does not use any pilot symbols.…”

“…This includes: (i) the discussion and analysis of a naïve superimposed ASC scheme based on the application of the techniques in [4], (ii) the discovery of an error floor in this scheme due to a bounded signal-to-interference plus noise ratio (SINR), (iii) the proposal of an orthogonal code superimposed ASC scheme that removes the error floor, and provides better BER performance than superimposed PAT.…”