Experimental evaluation of postdetection diversity reception ofnarrow-band digital FM signals in Rayleigh fading

Postdetection diversity is attractive for narrowband digital FM signal reception because the cophasing function, which may be difficult to realize in a fast Rayleigh fading environment, is not required. The combining scheme evaluated here is to weight each frequency demodulator (FD) output in proportion to the νth power of the received signal envelope of that branch. Maximum diversity improvement can be obtained with ν=2 (this combiner is referred to as a postdetection maximal ratio chamber (MRC)). Experimental results are presented on postdetection diversity reception in the Gaussian minimum shift keying (GMSK) signal transmission system. Diversity combining and FD-decision algorithms (decision feedback equalizer (DFE) and maximum-likelihood sequence estimator (MLSE)) are performed by software on a computer using the data of the sampled FD output and received signal envelope obtained from a laboratory transmission system. It is shown that the MRC can attain about a 1-dB larger diversity gain than the selection combiner (SC) when two-branch diversity is used. The degradations of two-branch diversity improvement caused by the differences between demodulator sensitivities and between received signal envelope detector gains are evaluated     

Error analysis for nonuniform signaling over Rayleigh fading channels

We investigate the error performance of a communication system where a nonuniform memoryless binary source is transmitted via Gray-mapped M-ary phase-shift keying or quadrature amplitude modulation over memoryless Rayleigh fading channels, and demodulated via optimal maximum a posteriori detection. Using recently derived upper and lower bounds on the probability of a general union of events, which are tight and can be efficiently computed, the system symbol-error (P/sub s/) and bit-error (P/sub b/) rates are evaluated for a wide range of channel conditions. Since for nonuniform signaling, Gray mapping is not necessarily optimal for minimizing P/sub s/ or P/sub b/ (as was recently shown by Takahara et al.), we also evaluate the system performance under the map obtained by Takahara et al. and compare it with a Gray-mapped system.     

Transmission of digital data over a Rayleigh fading channel

In a microwave mobile telecommunications system, a digital message must be transmitted several times to overcome the effects of Rayleigh fades that characterize this channel, and thus ensure a high probability that the message is received error-free. Obviously, there are many different transmission schemes that may be suitable for this channel. We present an analytic approach to an evaluation of their comparative performance in terms of the probability of a transmission failure, and provide a basis for the design of an efficient scheme. In the first part, we present some fade statistics that have been used in our analysis. Next, we derive upper bounds on the probability of the transmission failure for three different schemes. The actual failure rates as determined in an experimental simulation are then shown for those schemes that our theoretical study predicts to be acceptable. It is shown that an efficient scheme for the Rayleigh fading channel is the block-protected one in which a message is transmitted four times, each transmission 4-ms long and spaced 4-ms apart. The spacing is obtained by interleaving a similar transmission of another message. The receiver discards a transmission if it fails the parity checks.     

Error probability performance of L-branch diversity reception ofMQAM in Rayleigh fading

New exact expressions involving hypergeometric functions are derived for the symbol-error rate (SER) of M-ary quadrature amplitude modulation (MQAM) for L branch diversity reception in Rayleigh fading and additive white Gaussian noise (AWGN). The diversity combining techniques considered are maximum ratio combining (MRC) and selection combining (SC). MRC with identical channels and dissimilar channels are analyzed     

Error performance of interleaved trellis-coded PSK modulations incorrelated Rayleigh fading channels

The authors derive an exact and easily computed expression for the pairwise error event probability of interleaved coded PSK modulations transmitted over channels with correlated Rayleigh flat fading and additive white Gaussian noise. Both coherent and differential detection are considered. In the case of coded DPSK, it is found that full interleaving does not necessarily provide the best error performance, especially when the fading is relatively fast and when the autocorrelation function of the channel fading process exhibits an oscillating behavior. For coherent detection or for differential detection in channels with relatively slow fading, increasing the interleaving depth always improves the error performance. In these cases, an interleaving depth equivalent to one-fifth to one-quarter the duration of a fade cycle is almost as good as full interleaving     

A formula for an FM signal under Rayleigh fading [mobile radio]

A simple formula for the baseband signal-to-noise ratio of an FM signal under Rayleigh fading is derived. The formula automatically includes the noise component due to modulation. Calculated values of the average signal-to-noise ratio for FM and AM signals under Rayleigh fading are given. The results show that the FM signal with a modulation index of one or greater, outperforms an AM signal under identical fading conditions     

Rayleigh fading channels in mobile digital communication systems.I. Characterization

The paper addresses Rayleigh fading, primarily in the UHF band, that affects mobile systems such as cellular and personal communication systems (PCS). The paper itemizes the fundamental fading manifestations and types of degradation. Two types of fading, large-scale and small-scale, are described. Two manifestations of small-scale fading (signal dispersion and fading rapidity) are examined, and the examination involves two aspects: time and frequency. Two degradation categories are defined for dispersion: frequency selective fading and flat fading. Two degradation categories are defined for fading rapidity: fast and slow. A mathematical model using correlation and power density functions is presented. This model yields a symmetry to help view the Fourier transform and duality relationships that describe the fading phenomena     

Rayleigh fading channels in mobile digital communication systems.II. Mitigation

For pt. I see ibid., vol. 35, no. 7, p. 90, 1997. In Part I of this tutorial, the major elements that contribute to fading and their effects in a communication channel were characterized. In Part II, these phenomena are briefly summarized, and emphasis is then placed on methods to cope with these degradation effects. Two particular mitigation techniques are examined: the Viterbi equalizer implemented in the Global System for Mobile Communication (GSM), and the RAKE receiver used in CDMA systems built to meet Interim Standard 95 (IS-95)     

Rayleigh fading channels in mobile digital communication systems.I. Characterization

When the mechanisms of fading channels were first modeled in the 1950s and 1960s, the ideas were primarily applied to over-the-horizon communications covering a wide range of frequency bands. The 3-30 MHz high-frequency (HF) band is used for ionospheric communications, and the 300 MHz-3 GHz ultra-high-frequency (UHF) and 3-30 GHz super-high-frequency (SHF) bands are used for tropospheric scatter. Although the fading effects in a mobile radio system are somewhat different than those in ionospheric and tropospheric channels, the early models are still quite useful to help characterize fading effects in mobile digital communication systems. This tutorial addresses Rayleigh fading primarily in the UHF band. That affects mobile systems such as cellular and personal communication systems (PCS). Part I of the tutorial itemizes the fundamental fading manifestations and types of degradation     

Performance of feedback and switch space diversity 900 MHz FM mobile radio systems with Rayleigh fading

A theoretical and experimental comparison of performance has been made between two types of predetection switching space diversity mobile radio systems. This comparison was made at a frequency of 840 MHz using simulated Rayleigh fading for a vehicle speed of about 80 mi/h. The switch diversity system was a conventional receiver antenna switching technique with two simulated physically separated receiving antennas and a single transmitting antenna. The feedback diversity system used a single receiving antenna with two simulated physically separated transmitting antennas. The transmitting antennas were switched remotely from the receiver. The difference in the performance of the two systems was shown to be primarily due to time delay inherent in the remote antenna switching technique.     

Error rate performance of digital FM mobile radio withpostdetection diversity

An analysis of bit error rate (BER) in a binary digital FM system with postdetection diversity is presented. Expressions for the average BER due to additive white Gaussian noise (AWGN), random FM noise and delay-spread in the multipath channel are derived for reception using differential demodulation (DD), and frequency demodulation (FD) assuming independent fading signals. Calculated results for MSK show that the BER performance is strongly dependent on the RMS-delay/bit-duration ratio and that the delay-spectrum shape is of no importance when the receiver predetection filter product is optimized for the effect of AWGN. The effect of fading correlation on the diversity improvement is also analyzed for a two-branch case with multiplicative Rayleigh fading signals. Expressions for the average BER due to AWGN and random FM noise are derived. Calculated results are shown for the average BER due to random FM noise assuming a horizontally spaced antenna system at a mobile station. It is shown that the use of small antenna spacings leads to a diversity improvement greater than that obtainable for the case of independent AWGN     

Error probability of Q-ary symbol consisting of multiple channel symbols under Rayleigh fading

Closed-form expressions for symbol error probabilities are derived for the case when modulation alphabet size M is smaller than symbol size Q. We consider slow Rayleigh fading channel where fading amplitudes and phases remain constant during one Q-ary symbol duration. An exact expression is obtained for noncoherent M-ary frequency-shift keyed (MFSK) modulation and the simple and accurate approximate expressions are obtained for M-ary phase-shift keyed (MPSK) and quadrature-amplitude modulation. Simulation results showed that the derived error probability are well agreed.     

On the use of Reed-Solomon codes in improving digital FMtransmission performance in Rayleigh fading

Reed Solomon codes with interleaving are used in a binary FM transmission affected by Rayleigh fading as encountered in land mobile radio. A new decoding algorithm is proposed which can be implemented in simple hardware. The error performance of the binary FM system with the RS code with one and two degrees of interleaving is measured. A significant reduction of error rate floor as a function of fading speed is noted and discussed     

Performance of an in-band adjacent-channel DAB system forfrequency-selective Rayleigh and Ricean slow fading channels underanalog FM interference

In support of the 1995-1997 DAB (digital audio broadcasting) testing conducted by the NRSC (National Radio Systems Committee), an IBAC (in-band adjacent-channel) scheme was developed by AT&T. Although not for use in the United States, bit error rate (BER) system performance under both fading environments and the existing analog FM broadcasting is important to quantify. This is because there may still exist other countries and environments where an IBAC approach to DAB is feasible and economical. Given this situation, an IBAC simulation model has been developed to allow for a performance analysis study within the mobile reception environment, which is dominated by Rayleigh and Ricean fading statistics. This paper presents the simulation results for coherent quadrature phase-shift-keying (QPSK) with nonlinear equalization for both frequency-selective Rayleigh and Ricean slow fading channel environments, along with co-channel, 1st-adjacent and 2nd-adjacent analog FM interference. The results indicate that for a country where spectrum availability dictates an IBAC solution, this approach may perform well under various fading and interference environments     

Error performance of matched and partially matched one-shotdetectors for doubly selective Rayleigh fading channels

In this paper, optimum one-shot detection over known and partially known doubly selective Rayleigh fading channels is investigated. Reduced complexity channel models based on Gauss quadrature rules and Taylor power series are derived and are employed to develop novel analytical tools for the performance analysis of one-shot detectors. Numerical results allow to assess the implicit diversity gain provided by both channel multipath and signal fading and the energy loss due to the mismatch of the receiver filter     

Error performance of multiple-symbol differential detection of PSKsignals transmitted over correlated Rayleigh fading channels

The error performance of multiple-symbol differential detection of uncoded QPSK signals transmitted over correlated Rayleigh fading channels is studied. The optimal detector is presented, along with an exact expression for the corresponding pairwise error event probability. It is shown that multiple-symbol differential detection is a very effective strategy for eliminating the irreducible error floor associated with a conventional differential detector. In all of the cases investigated, a detector with an observation interval as small as two symbols is sufficient for this purpose. It is also found that the error performance of a multiple-symbol differential detector is not sensitive to the mismatch between the decoding metric and the channel fading statistics     

Error rates of DPSK systems with MIMO EGC diversity reception over Rayleigh fading channels

This paper analyzes the average bit error probability (BEP) of the differential binary and quaternary phase-shift keying (DBPSK and DQPSK respectively) with multiple-input multiple-output (MIMO) systems employing postdetection equal gain combining (MIMO EGC) diversity reception over Rayleigh fading channels. Finite closed-form expressions for the average BEP of DBPSK and DQPSK are presented. Two approaches are introduced to analyze the error rate of DQPSK. The proposed structure for the differential phase-shift keying (DPSK) with MIMO EGC provides a reduced-complexity and low-cost receiver for MIMO systems compared to the coherent phase-shift keying system (PSK) with MIMO employing maximal ratio combining (MIMO MRC) diversity reception. Finally, a useful procedure for computing the associated Legendre functions of the second kind with half-odd-integer order and arbitrarily degree is presented.     

Switched-diversity FSK in frequency-selective Rayleigh fading

This paper presents the measured performance of a 64 kbit/s switched-diversity FSK receiver subjected to simulated frequency-selective Rayleigh fading. The single receiver input is switched between two, three, or four uncorrelated Rayleigh-fading signals whenever the instantaneous receiver output falls below a threshold. The optimum level of this threshold relative to the mean signal level is relatively insensitive to frequency selectivity and vehicle speed. A nearly optimum threshold may be determined using an AGC amplifier and fixed comparator. Switched diversity is a powerful tool for combating frequency selectivity and Rayleigh fading. Two-branch switched diversity can achieve 10^-2BER, with 6 dB lower SNR than that needed without diversity. In the absence of frequency selectivity, two-branch switched diversity can perform within 3 dB SNR of maximal-ratio diversity and within 1 dB of selection diversity. Switched diversity can achieve BER's lower than the irreducible single-channel BER produced by frequency selectivity. Four-branch switched diversity typically requires 4 dB lower SNR to achieve a given BER than does two-branch switched diversity.     

Error performance of selection combining and switched combining systems in Rayleigh fading channels with imperfect channel estimation

In this paper, we present a general analysis of the performance of selection combining (SC), switch-and-stay combining (SSC), and switch-and-examine combining (SEC) systems in Rayleigh fading channels with imperfect channel estimation (ICE). The complex channel estimate and the actual fading are modeled as jointly Gaussian random variables. For SC systems with channel estimation error, closed-form expressions are obtained for the error rates of M/sub s/-ary pulse amplitude modulation (PAM) and rectangular-quadrature amplitude modulation (QAM), and simple single integral formulas with finite integration limits are derived for the symbol error probability of arbitrary two-dimensional (2-D) modulation formats. These error probability expressions are then applied to three types of channel estimation errors potentially encountered in practical systems to study their impact on the performance of selection diversity. Moreover, single integral formulas with finite integration limits are derived for the performance of SSC and SEC systems with minimum mean square error (MMSE) channel estimation. Optimum switching thresholds for 2-D modulation formats with MMSE based switched combining are acquired through numerical computation.     

Analysis of transmit-receive diversity in Rayleigh fading

We analyze the error performance of a wireless communication system employing transmit-receive diversity in Rayleigh fading. By focusing on the complex Gaussian statistics of the independent and identically distributed entries of the channel matrix, we derive a formula for the characteristic function (c.f.) of the maximum output signal-to-noise ratio. We use this c.f. to obtain a closed-form expression of the symbol error probability (SEP) for coherent binary keying. The method is easily extended to obtain the SEP for the coherent reception of M-ary modulation schemes.