There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Wireless Communications

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Table Of Integrals Series And Products

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth.

/pdf/random-matrix-theory-and-wireless-communications-lhkk3xrf4v.pdf

Random Matrix Theory and Wireless Communications

High peak-to-average power ratio of the transmit signal is a major drawback of multicarrier transmission such as OFDM or DMT. This article describes some of the important PAPR reduction techniques for multicarrier transmission including amplitude clipping and filtering, coding, partial transmit sequence, selected mapping, interleaving, tone reservation, tone injection, and active constellation extension. Also, we make some remarks on the criteria for PAPR reduction technique selection and briefly address the problem of PAPR reduction in OFDMA and MIMO-OFDM.

An overview of peak-to-average power ratio reduction techniques for multicarrier transmission

The capacity of multiple-input multiple-output (MIMO) wireless channels is limited by both the spatial fading correlation and rank deficiency of the channel. While spatial fading correlation reduces the diversity gains, rank deficiency due to double scattering or keyhole effects decreases the spatial multiplexing gains of multiple-antenna channels. In this paper, taking into account realistic propagation environments in the presence of spatial fading correlation, double scattering, and keyhole effects, we analyze the ergodic (or mean) MIMO capacity for an arbitrary finite number of transmit and receive antennas. We assume that the channel is unknown at the transmitter and perfectly known at the receiver so that equal power is allocated to each of the transmit antennas. Using some statistical properties of complex random matrices such as Gaussian matrices, Wishart (1928) matrices, and quadratic forms in the Gaussian matrix, we present a closed-form expression for the ergodic capacity of independent Rayleigh-fading MIMO channels and a tight upper bound for spatially correlated/double scattering MIMO channels. We also derive a closed-form capacity formula for keyhole MIMO channels. This analytic formula explicitly shows that the use of multiple antennas in keyhole channels only offers the diversity advantage, but provides no spatial multiplexing gains. Numerical results demonstrate the accuracy of our analytical expressions and the tightness of upper bounds.

/pdf/capacity-of-multiple-antenna-fading-channels-spatial-fading-3dbfx5f65g.pdf

Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole

A major drawback of orthogonal frequency division multiplexing (OFDM) is the high peak-to-average power ratio (PAPR) of the transmitted signal. Partial transmit sequence (PTS) technique can improve the PAPR statistics of OFDM signals. In the PTS technique, the data block to be transmitted is partitioned into disjoint subblocks and the subblocks are combined using phase factors to minimize PAPR. As ordinary PTS technique requires an exhaustive search over all combinations of allowed phase factors, the search complexity increases exponentially with the number of subblocks. In the proposed technique, a gradient descent search is performed to find the phase factors. It is shown that the proposed technique achieves significant reduction in search complexity with little performance degradation.

/pdf/papr-reduction-of-ofdm-signals-using-a-reduced-complexity-3zz9cv0zqw.pdf

PAPR reduction of OFDM signals using a reduced complexity PTS technique

In multiple-input-multiple-output (MIMO) fading environments, degenerate channel phenomena, called keyholes or pinholes, may exist under the realistic assumption that the spatial fading is uncorrelated at the transmitter and the receiver, but the channel has a rank-deficient transfer matrix. In this paper, we analyze the exact average symbol error rate (SER) of orthogonal space-time block codes (STBCs) with M-PSK and M-QAM constellations over Nakagami-m fading channels in the presence of the keyhole. We derive the moment generating function (MGF) of instantaneous signal-to-noise ratio (SNR) after space-time block decoding (signal combining) in such channels. Using a well-known MGF-based analysis approach, we express the average SER of the STBC in the form of single finite-range integrals whose integrand contains only the derived MGF. Numerical results show that the keyhole significantly degrades the SER performance of the STBC from idealistic behaviors in independent identically distributed MIMO channels.

/pdf/performance-analysis-of-space-time-block-codes-over-keyhole-uywg0p4id9.pdf

Performance analysis of space-time block codes over keyhole Nakagami-m fading channels

In this paper, we analyze the capacity of multiple-input multiple-output (MIMO) Rayleigh-fading channels in the presence of spatial fading correlation at both the transmitter and the receiver, assuming the channel is unknown at the transmitter and perfectly known at the receiver. We first derive the determinant representation for the exact characteristic function of the capacity, which is then used to determine the trace representations for the mean, variance, skewness, kurtosis, and other higher-order statistics (HOS). These results allow us to exactly evaluate two relevant information-theoretic capacity measures - ergodic capacity and outage capacity - and the HOS of the capacity for such a MIMO channel. The analytical framework presented in the paper is valid for arbitrary numbers of antennas, and generalizes the previously known results for independent and identically distributed or one-sided correlated MIMO channels to the case when fading correlation exists on both sides. We verify our analytical results by comparing them with Monte Carlo simulations for a correlation model based on realistic channel measurements as well as a classical exponential correlation model

/pdf/on-the-capacity-of-doubly-correlated-mimo-channels-os8oxi9v7p.pdf

Jae Hong Lee

Papers

An overview of peak-to-average power ratio reduction techniques for multicarrier transmission

Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole

PAPR reduction of OFDM signals using a reduced complexity PTS technique

Performance analysis of space-time block codes over keyhole Nakagami-m fading channels

On the capacity of doubly correlated MIMO channels