Cross Z-Complementary Pairs for Optimal Training in Spatial Modulation Over Frequency Selective Channels

The contributions of this article are twofold: Firstly, we introduce a novel class of sequence pairs, called “cross Z-complementary pairs (CZCPs),” each displaying zero-correlation zone (ZCZ) properties for both their aperiodic autocorrelation sums and crosscorrelation sums. Systematic constructions of perfect CZCPs based on selected Golay complementary pairs (GCPs) are presented. Secondly, we point out that CZCPs can be utilized as a key component in designing training sequences for broadband spatial modulation (SM) systems. We show that our proposed SM training sequences derived from CZCPs lead to optimal channel estimation performance over frequency-selective channels

Spatial encoding in primate hippocampus during free navigation.

The hippocampus comprises two neural signals-place cells and θ oscillations-that contribute to facets of spatial navigation. Although their complementary relationship has been well established in rodents, their respective contributions in the primate brain during free navigation remains unclear. Here, we recorded neural activity in the hippocampus of freely moving marmosets as they naturally explored a spatial environment to more explicitly investigate this issue. We report place cells in marmoset hippocampus during free navigation that exhibit remarkable parallels to analogous neurons in other mammalian species. Although θ oscillations were prevalent in the marmoset hippocampus, the patterns of activity were notably different than in other taxa. This local field potential oscillation occurred in short bouts (approximately .4 s)-rather than continuously-and was neither significantly modulated by locomotion nor consistently coupled to place-cell activity. These findings suggest that the relationship between place-cell activity and θ oscillations in primate hippocampus during free navigation differs substantially from rodents and paint an intriguing comparative picture regarding the neural basis of spatial navigation across mammals

A Direct Construction of Optimal Symmetrical Z-Complementary Code Sets of Prime Power Lengths

This paper presents a direct construction of an optimal symmetrical Z-complementary code set (SZCCS) of prime power lengths using a multi-variable function (MVF). SZCCS is a natural extension of the Z-complementary code set (ZCCS), which has only front-end zero correlation zone (ZCZ) width. SZCCS has both front-end and tail-end ZCZ width. SZCCSs are used in developing optimal training sequences for broadband generalized spatial modulation systems over frequency-selective channels because they have ZCZ width on both the front and tail ends. The construction of optimal SZCCS with large set sizes and prime power lengths is presented for the first time in this paper. Furthermore, it is worth noting that several existing works on ZCCS and SZCCS can be viewed as special cases of the proposed construction

Root Cross Z-Complementary Pairs with Large ZCZ Width

In this paper, we present a new family of cross $Z$-complementary pairs (CZCPs) based on generalized Boolean functions and two roots of unity. Our key idea is to consider an arbitrary partition of the set $\{1,2,\cdots, n\}$ with two subsets corresponding to two given roots of unity for which two truncated sequences of new alphabet size determined by the two roots of unity are obtained. We show that these two truncated sequences form a new $q$-ary CZCP with flexible sequence length and large zero-correlation zone width. Furthermore, we derive an enumeration formula by considering the Stirling number of the second kind for the partitions and show that the number of constructed CZCPs increases significantly compared to the existing works.Comment: This work has been presented in 2022 IEEE International Symposium on Information Theory (ISIT), Espoo, Finlan

Soft-decision equalization techniques for frequency selective MIMO channels

Multi-input multi-output (MIMO) technology is an emerging solution for high data rate wireless communications. We develop soft-decision based equalization techniques for frequency selective MIMO channels in the quest for low-complexity equalizers with BER performance competitive to that of ML sequence detection. We first propose soft decision equalization (SDE), and demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered, and linear in the signal constellation size. Building upon the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Motivated by the need for low-complexity receiver processing, we further present an alternative low-complexity soft-decision equalization approach for frequency selective MIMO communication systems. With the help of iterative processing, two detection and estimation schemes based on second-order statistics are harmoniously put together to yield a two-part receiver structure: local multiuser detection (MUD) using soft-decision Probabilistic Data Association (PDA) detection, and dynamic noise-interference tracking using Kalman filtering. The proposed Kalman-PDA detector performs local MUD within a sub-block of the received data instead of over the entire data set, to reduce the computational load. At the same time, all the inter-ference affecting the local sub-block, including both multiple access and inter-symbol interference, is properly modeled as the state vector of a linear system, and dynamically tracked by Kalman filtering. Two types of Kalman filters are designed, both of which are able to track an finite impulse response (FIR) MIMO channel of any memory length. The overall algorithms enjoy low complexity that is only polynomial in the number of information-bearing bits to be detected, regardless of the data block size. Furthermore, we introduce two optional performance-enhancing techniques: cross- layer automatic repeat request (ARQ) for uncoded systems and code-aided method for coded systems. We take Kalman-PDA as an example, and show via simulations that both techniques can render error performance that is better than Kalman-PDA alone and competitive to sphere decoding. At last, we consider the case that channel state information (CSI) is not perfectly known to the receiver, and present an iterative channel estimation algorithm. Simulations show that the performance of SDE with channel estimation approaches that of SDE with perfect CSI

Digital signal processing techniques for peak-to-average power ratio mitigation in MIMO–OFDM systems

The focus of this thesis is to mitigate the very large peak-to-average transmit power ratios (PAPRs) inherent to conventional orthogonal frequency division multiplexing (OFDM) systems, particularly in the context of transmission over multi-input multi-output (MIMO) wireless broadband channels. This problem is important as a large PAPR generally needs an expensive radio frequency (RF) power amplifier at the transmitter due to the requirement for linear operation over a wide amplitude range and such a cost would be compounded when multiple transmit antennas are used. Advanced signal processing techniques which can reduce PAPR whilst retain the integrity of digital transmission therefore have considerable potential for application in emergent MIMO–OFDM wireless systems and form the technical contributions of this study. [Continues.