Vasant K. Prabhu

Analysis of equal-gain diversity with partially coherent fading signals

An analytical technique based on Gram-Charlier series expansion is presented for the computation of the error probability of equal-gain combiner (EGC) with partially coherent fading signals. Imperfect carrier recovery is attributed to the random noise present in the carrier recovery loops. The resulting noisy phase references are assumed to satisfy Tikhonov distribution. The fades on the diversity branches are assumed to be slowly varying and statistically independent with Rayleigh-distributed envelopes. The error-rate performance of coherent and differentially coherent phase-shift keying (PSK) systems are compared and the phase precision requirement for a reliable coherent detection is computed. Detection loss caused by carrier phase errors is computed for several signal-to-noise ratio (SNR) reliability and bit error probability levels. It is demonstrated that the effect of carrier phase errors on the mean SNR is negligible compared to their effect on deep fades or small bit error probabilities. It is also shown that the carrier phase precision requirement can be reduced through signal combination.

Performance analysis of generalized-faded coherent PSK channels with equal-gain combining and carrier phase error

A new method is developed to analyze the performance of partially coherent PSK systems in wireless channels with equal-gain combining diversity receiver. Two performance criteria are considered: the average bit error probability and the probability distribution of the combiner SNR (SNR reliability). Tikhonov-distributed phase error processes are assumed and generalized fading channels including Rayleigh, Rician, and Nakagami-m are investigated. We evaluate the detection loss suffered by the carrier recovery for different SNR reliability levels when BPSK and QPSK systems are used in wireless channels. The analysis is based on a convergent infinite series for the distribution of the sum of random variables. The convergence rate of the proposed series is investigated and the analytical results are presented along with providing results obtained by simulation.

Power spectral density of GMSK modulation using matrix methods

Gaussian minimum shift keying (GMSK) modulation is widely used in cellular and PCS applications. The popular GSM system uses GMSK. One of the important considerations in the use of modulation is the average power spectral density (PSD) and especially the spectral density characteristics on the tails. No method, other than simulation, is currently available to determine the PSD of GMSK. In this paper we give closed form expressions for computing the power spectrum using vector-matrix techniques. The PSD is expressed in a compact Hermitian form suitable for numerical computation. The PSD can be calculated to any desired accuracy by using this method. Results are given for various Gaussian baseband filter bandwidth-time products and modulation pulse truncation lengths. The formulas given in this paper can be extended to arbitrary pulse shapes and arbitrary modulation indices.

Optimum sectorization for CDMA 1900 base stations

Since minimizing the co-channel interference in the conventional cellular technologies (AMPS, TDMA, and GSM) leads to better spectral efficiency, these technologies require a systematic frequency planning scheme. Generally, cells are grouped in a cluster of 7 (N=7). Each cluster reuses the same frequency to maximize bandwidth efficiency. To further minimize the co-channel interference from adjacent clusters, sector antennas are used. A cell is typically sectorized into three sectors (K=3) to achieve rapid frequency reuse. The deployment practices include using the N=7, K=3 or using the N=4, K=6 frequency reuse scheme. Because of the flexibility of the CDMA technology, restrictions of using the conventional clusterization and/or sectorization schemes may not be warranted. In fact, to maximize the utilization of existing resources such as cell-site equipment, structures, real-estate, backhauls, etc., employing a non-standard sectorization scheme will yield a more optimum configuration and a more cost-effective solution. We address such non-standard sectorizations.

Performance evaluation for widely linear demodulation of PAM/QAM signals in the presence of rayleigh fading and co-channel interference

In this paper, widely linear filtering (WLF) techniques are applied to the demodulation of both pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) systems with multiple receiver antennas and multiple cochannel interferers. In the proposed implementation, the existing correlations between the real (I) and imaginary (Q) parts of the complex-valued baseband received signal are exploited using a widely linear (WL) maximum likelihood (ML) receiver. Several bounds and approximations are developed to analyze the average symbol error rate (SER) performance, and to analyze the tradeoff between the diversity advantage and interference cancellation (IC) gain in a flat Rayleigh fading channel. Two new results are shown. First, we show that the IC ability of WL receivers is independent of the modulation type used by the desired signal but the gain depends mainly on the modulation type employed by the individual interferers and the total number of antennas. Secondly, assuming that the system uses a mixture of PAM and QAM signals, we show that a WL receiver with N antennas can reject any combination of M1 PAM, M2 QAM interferers satisfying the constraint: M1 + 2M2 < 2N with an asymptotic diversity order N - M1/2 - M2. In contrast, a conventional receiver whose performance is independent of the modulation characteristics of the individual interferers can reject only up to M1 + M2 interferers, where M1 + M2 < N with an asymptotic diversity order N - M1 - M2. When the system contains either PAM, or a mixture of PAM and QAM type CCI, it is shown that WL processing offers a significant performance advantage with a moderate increase in the receiver complexity.

Performance analysis of PSK systems in the presence of slow fading, imperfect carrier phase recovery, and AWGN

Using Fourier series expansion and associated Legendre functions, the average bit error probability (BEP) of the binary and quaternary phase shift keying (BPSK and QPSK respectively) on a single channel (no diversity) in the presence of different kinds of slow fading channels (Rayleigh, Nakagami-m, and Rician), phase recovery error, and additive white Gaussian noise (AWGN) has been evaluated. The detection loss for both of BPSK and QPSK has been calculated. The series expressions of the average BEP proposed in our study are found to be converged with reasonable number of terms. The accuracy of the results is verified by computer simulation. Although our approach is devoted for the PSK systems, it can be easily extended to other modulation schemes and noise impairments

Capacity growth for CDMA system: multiple sectors and multiple carriers deployment

Due to the increasing acceptability of CDMA, all infrastructure/service providers are accelerating their investigation to map out strategies to handle the increasing capacity demand. In the AMPS/TDMA technology, cell splitting has been one of the standard practices to improve the frequency reuse factor in order to increase capacity. Furthermore, dynamic channel/resource allocation has been demonstrated to provide capacity relief in localized hot spots. In the CDMA technology, however, since the conventional AMPS/TDMA frequency planning is not required, there are new strategies to increase capacity. Previously, Wong and Prabhu (see IEEE VTC, p.1177-81, 1997) had investigated the optimum sectorization scheme for a CDMA base station to provide higher capacity. Multiple carriers deployment provides another option. From a capacity standpoint, even an un-orchestrated multiple carriers deployment multiplies the capacity of the network. With an intelligent resource allocation scheme, the traffic loading among multiple carriers can be intelligently managed to increase the trunking efficiency of the network. It results in much higher aggregated Erlang capacity and better system redundancy.

A successive interference cancellation multiuser detector for MIMO CDMA systems

Multiuser detection in CDMA systems has been well researched since the pioneering work by Verdu that demonstrated the huge potential increase in capacity that multiuser detectors provide over conventional detectors. Some sub-optimal but easily implementable multiuser detectors for single input single output (SISO) systems have been researched. One such detector is the successive interference cancellation (SIC) multiuser detector. In this paper, we propose a simple extension of the SIC multiuser detector to CDMA VBLAST multiple input multiple output (MIMO) systems. We demonstrate the benefits of the SIC multiuser detector over the conventional detector for a few transmit-receive configurations. Further, the effect of thermal noise power on the performance of the SIC multiuser detector has also been shown.

Dynamic system simulator for the modeling of CDMA systems

As wireless systems progressed from first generation to second generation, and now 3G systems, system design tools have progressively become more sophisticated. Static system simulators have found widespread use in CDMA system design. In this article it is argued that static simulators are inadequate to capture the details of 3G systems, and study the performance of complex algorithms, and the case is made for dynamic system simulators. A detailed description of the structure of a wireless system simulator is given, with emphasis on a dynamic simulator. Some advantages of dynamic vs. static simulators are discussed.

Average level crossing rates and average fade durations for maximal-ratio combining in correlated Nakagami channels

For uncorrelated Nakagami channels in wireless systems, the level crossing rates (LCKs) and average fade durations (AFDs) of maximum ratio combining have been derived. However, this assumption is usually violated in the real world. In this paper, we derive the LCRs and AFDs for correlated Nakagami channels, which have not been addressed in the literature. Simulation results demonstrate that the LCRs and AFDs of the correlation signals are larger than those of the uncorrelated signals at lower levels. Furthermore, the effects of fading severity of the channel and the number of diversity branches on the LCRs and AFDs are also studied.