Uniform Power Delay Profile Research Articles

Coherent Detection of Turbo-Coded OFDM Signals Transmitted Through Frequency Selective Rayleigh Fading Channels with Receiver Diversity and Increased Throughput

In this work, we discuss techniques for coherently detecting turbo coded orthogonal frequency division multiplexed (OFDM) signals, transmitted through frequency selective Rayleigh (the magnitude of each channel tap is Rayleigh distributed) fading channels having a uniform power delay profile. The channel output is further distorted by a carrier frequency and phase offset, besides additive white Gaussian noise (AWGN). A new frame structure for OFDM, consisting of a known preamble, cyclic prefix, data and known postamble is proposed, which has a higher throughput compared to the earlier work. A robust turbo decoder is proposed, which functions effectively over a wide range of signal-to-noise ratio (SNR). The key contribution to the good performance of the practical coherent receiver is due to the use of a long preamble (512 QPSK symbols), which is perhaps not specified in any of the current wireless communication standards. We have also shown from computer simulations that, it is possible to obtain even better BER performance, using a better code. A simple and approximate Cramer-Rao bound on the variance of the frequency offset estimation error for coherent detection, is derived. The proposed algorithms are well suited for implementation on a DSP-platform.

On the Practical Implementation of VFDM-based Opportunistic Systems: Issues and Challenges

Vandermonde-subspace frequency division multiplexing (VFDM) is a physical layer technique for cognitive two-tiered networks, allowing for the coexistence of an orthogonal frequency division multiplexing (OFDM) legacy system and a cognitive secondary system in a time division duplex mode. It consists of a linear null-space precoder used by the secondary transmitter to effectively cancel the interference towards one or more primary receivers, while guaranteeing a non-negligible rate to a served secondary receiver. In this work, we propose an implementation of an experimental test-bed using the new SDR4All platform developed at the Alcatel-Lucent Chair on Flexible Radio (SUPELEC) to take a step towards a proof of concept of a VFDM-based system. We focus on the secondary link, where an opportunistic transmitter/receiver pair communicates over moderately frequency selective channels, characterized by very short root mean square (r.m.s.) delay spreads and non uniform power delay profiles (PDP). The obtained results show the practical feasibility of a VFDM transmission over a secondary link. However, a significant bit error rate (BER) loss with respect to the previously shown achievable theoretical performance is evident. A thorough analysis of the structure of the VFDM precoder is carried out and the impact of the channel characteristics on the performance of the opportunistic system is discussed. Numerical findings demonstrate that the potential BER drop can be addressed by designing a suitable flexible receiver able to deal with the effect induced by non uniform PDP and short r.m.s. delay spread channels.

Distributed Space-Frequency Coding for Cooperative Diversity Over Broadband Relay Channels With DF Relaying

Multipath fading is one of the main challenges in transmission over wireless broadband relay channels due to frequency selectivity, which may deteriorate the received signal. Exploiting the extra source of multipath diversity, aside from cooperative (user) diversity, is important when coping with these wireless channel limitations. In this correspondence, we propose a new distributed space-frequency code (SFC) for broadband fading relay channels that can exploit both the spatial and multipath diversities in a distributed fashion. An upper bound for pairwise error probability (PEP) is derived, and from this PEP bound, we show that the proposed code achieves a diversity of order <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NL</i> , where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of relay nodes, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> is the channel memory length. The decode-and-forward (DF) protocol and erroneous decoding at the relay nodes are considered. Moreover, it is shown that the proposed code structure achieves the maximum coding gain among the linearly coded systems over channels with uniform power delay profiles.

Passive Phase Conjugation Applied to an OFDM-Based Terrestrial Communication System

The demand for high-data-rate radio systems that can robustly operate in multipath environments presents challenging technical issues. In this paper, we propose a passive phase conjugation (PPC)-based orthogonal frequency-division multiplexing (OFDM) system. Compared with the conventional OFDM system, the proposed system achieves lower computational complexity since the need for conventional channel estimation and equalization can be eliminated. The performance gain of the proposed technique is shown to be particularly advantageous in systems with multiple receiver array elements. Numerical results are provided to illustrate the performance of the system when operating through a multipath radio channel. We also derive a closed-form formula that can be used to predict the performance of the proposed scheme over multipath channels with a uniform power delay profile. Our analysis validates the simulation results and provides insights into the behavior of wireless centric OFDM-PPC systems.

Optimum pilot-to-data power ratio for partial RAKE receiver in Nakagami-m fading channels

In this paper, we study the problem of optimizing the pilot-to-data power ratio (PDR) for uplink code-division multiple access (CDMA) systems with partial RAKE (PRAKE) receivers. Both code-division multiplex (CDM) and time-division multiplex (TDM) reference-assisted schemes are considered. We assume Nakagami-m fading channel with two types of power delay profile (PDP): uniform and exponential PDPs. The optimum PDR is derived via minimizing the upper bound of the probability of bit error. A closed-form expression for the optimum PDR is obtained for both CDM and TDM schemes with uniform PDP. For exponential PDP, we derive the condition satisfied by the optimum PDR and obtain it numerically. It is observed that the optimum PDR is noticeably affected by the decay factor, but not by the m-parameter. For exponential PDP, unlike for uniform PDP, the optimum PDR depends on the number of combined paths. We also show that the optimum PDR derived from the block-fading channel model performs favorably in the Jakes' model.

Analysis and Optimization of Pilot Symbol-Assisted Rake Receivers for DS-CDMA Systems

The effect of imperfect channel estimation (CE) on the performance of pilot-symbol-assisted modulation (PSAM) and MRC Rake reception over time- or frequency-selective fading channels with either a uniform power delay profile (UPDP) or a nonuniform power delay profile (NPDP) is investigated. For time-selective channels, a Wiener filter or linear minimum mean square error (LMMSE) filter for CE is considered, and a closed-form asymptotic expression for the mean square error (MSE) when the number of pilots used for CE approaches infinity is derived. In high signal-to-noise ratio (SNR), the MSE becomes independent of the channel Doppler spectrum. A characteristic function method is used to derive new closed-form expressions for the bit error rate (BER) of Rake receivers in UPDP and NPDP channels. The results are extended to two-dimensional (2-D) Rake receivers. The pilot-symbol spacing and pilot-to-data power ratio are optimized by minimizing the BER. For UPDP channels, elegant results are obtained in the asymptotic case. Furthermore, robust spacing design criteria are derived for the maximum Doppler frequency

On pilot-based multipath channel estimation for uplink CDMA systems: an overloaded case

The paper considers a coding scheme for multipath channel estimation in uplink code-division multiple-access systems where each user transmits an individual pilot signal (sequence) to estimate its multipath channel coefficients. Assuming a common radio channel model with a uniform power delay profile, we derive lower bounds on the maximum mean square error for two types of linear channel estimators: an inverse filter and a linear minimum mean square error (MMSE) estimator. In contrast to previous work, the main focus here is on overloaded systems where the total number of multipath channel coefficients of all users is greater than processing gain. We show that the inverse filter bound is attained if and only if each pilot sequence is a perfect root-of-unity sequence. Interestingly, the conventional matched filter achieves the same lower bound if pilot sequences form a complementary periodic sequence set. In case of the MMSE estimator, the lower bound is either met or not depending on some system parameters. We provide a necessary and sufficient condition for achieving the bound when pilot sequences are arbitrary vectors on the unit sphere. This paper gives insight into the performance limits of practical systems.

Properties of Space-Time Codes for Frequency-Selective Channels

Some important properties are derived for the diversity gain and the coding gain of space-time codes (STCs) for frequency-selective channels. It is proven that the diversity gain of a STC that provides maximum diversity gain for channels with a given number of taps is robust to a decrease in the number of taps. For coding gain analysis, we categorize the possible types of correlation matrices into several classes based on the type of power delay profile, spatial correlation, and tap correlation. It is proven that optimum STCs found for spatially independent and frequency-selective channels with uncorrelated taps and uniform power delay profile have coding gains that are robust against a mismatch in correlation structure if the number of taps is fixed. Thereafter, a systematic design procedure is applied to search for the best space-time trellis codes (STTCs) for frequency-selective channels. At a frame error rate (FER) of 0.01, our example 16-state binary phase-shift keying (BPSK) STTC outperforms the delay diversity code by 3.4 dB for a channel with three uncorrelated uniform taps. Further, the example STC designed for a channel with a given number of taps is shown to provide good performance for channels with fewer taps.