Analysis of Error Probability with Maximum Likelihood Detection over Discrete-Time Memoryless Noncoherent Rayleigh Fading Channels

It is known that the capacity of the discrete-time memoryless noncoherent Rayleigh fading channels (DTM-NRFC) is achieved by a discrete constellation with finite number of mass points and when one of the mass points is located at the origin 1]. In this paper, we present the maximum likelihood detection (MLD) error performance on DTM-NRFC for a discrete constellation with coding and spatial diversity. In the absence of outer coding, the error probability with MLD is derived in a surprisingly simple closed-form. On the other hand, with coding and diversity, our error probability expressions can be evaluated via saddle-point approximation techniques

The subject of place : staying with the trouble

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BER analysis of QAM on fading channels with transmit diversity

In this letter, we derive analytical expressions for the bit error rate (BER) of space-time block codes (STBC) from complex orthogonal designs (COD) using quadrature amplitude modulation (QAM) on Rayleigh fading channels. We take a bit log-likelihood ratio (LLR) based approach to derive the BER expressions. The approach presented here can be used in the BER analysis of any STBC from COD with linear processing for any value of M in an M-QAM system. Here, we present the BER analysis and results for a 16-QAM system with i) (2-Tx, L-Rx) antennas using Alamouti code (rate-1 STBC), ii) (3-Tx, L-Rx) antennas using a rate-1/2 STBC, and iii) (5-Tx, L-Rx) antennas using a rate-7/11 STBC. In addition to being used in the BER analysis, the LLRs derived can also be used as soft inputs to decoders for various coded QAM schemes, including turbo coded QAM with space-time coding as in high speed downlink packet access (HSDPA) in 3G

Multistream Distributed Cophasing

In this paper, we develop a distributed cophasing (DCP) technique for physical layer fusion of multiple data streams in a wireless sensor network with multiple destination nodes (DNs). The DNs can either be connected to a fusion center (referred to as centralized data processing; CDP) or process data independently and communicate with each other via a rate-limited link (referred to as distributed data processing; DDP). In the first stage of this two-stage cophasing scheme, sensors estimate the channel to the DNs using pilot symbols transmitted by the latter; following which they simultaneously transmit multiple streams of data symbols by prerotating them according to the estimated channel phases to the different DNs. The achievable rates for both CDP and DDP are derived to quantify the gains obtainable by the multistream DCP. In order to aid data detection at the receiver, we propose a least-squares-based iterative algorithm for blind channel estimation in CDP-DCP. Following this, we develop a message passing based blind channel estimation algorithm for DDP-DCP. It is found using Monte Carlo simulations that for the CDP system, the proposed blind channel estimation algorithm achieves a probability of error performance very close to that with perfect CSI at the DNs, while using only a moderate number of unknown data symbols for channel estimation. We also derive approximate expressions for the error probability performance of the proposed system for both CDP and DDP and validate their accuracy using Monte Carlo simulations

Physical Layer Data Fusion Via Distributed Co-Phasing With General Signal Constellations

This paper studies a pilot-assisted physical layer data fusion technique known as Distributed Co-Phasing (DCP). In this two-phase scheme, the sensors first estimate the channel to the fusion center (FC) using pilots sent by the latter; and then they simultaneously transmit their common data by pre-rotating them by the estimated channel phase, thereby achieving physical layer data fusion. First, by analyzing the symmetric mutual information of the system, it is shown that the use of higher order constellations (HOC) can improve the throughput of DCP compared to the binary signaling considered heretofore. Using an HOC in the DCP setting requires the estimation of the composite DCP channel at the FC for data decoding. To this end, two blind algorithms are proposed: 1) power method, and 2) modified K-means algorithm. The latter algorithm is shown to be computationally efficient and converges significantly faster than the conventional K-means algorithm. Analytical expressions for the probability of error are derived, and it is found that even at moderate to low SNRs, the modified K-means algorithm achieves a probability of error comparable to that achievable with a perfect channel estimate at the FC, while requiring no pilot symbols to be transmitted from the sensor nodes. Also, the problem of signal corruption due to imperfect DCP is investigated, and constellation shaping to minimize the probability of signal corruption is proposed and analyzed. The analysis is validated, and the promising performance of DCP for energy-efficient physical layer data fusion is illustrated, using Monte Carlo simulations