Impact of diversity reception on fading channels with codedmodulation. I. Coherent detection

We address the problem of designing and analyzing the performance of a coded modulation scheme for the fading channel when space diversity is used. Under fairly general conditions, a channel affected by fading can be turned into an additive white Gaussian noise (AWGN) channel by increasing the number of diversity branches. Consequently, it can be expected (and is indeed verified by our analyses and simulations) that a coded modulation scheme designed to be optimal for the AWGN channel also will perform asymptotically well on a fading channel with diversity. This paper presents bounds on the bit-error probability of a system with coded modulation and diversity for space- and time-correlated Rician flat fading. Specifically, we derive a new method which allows evaluation of the pairwise error probability extremely easily, as well as accurately and computationally fast. The accuracy achieved improves considerably on the widely used, but rather loose Chernoff bound. Starting from this analysis, we study the asymptotic behavior of the fading channel with diversity as the number of diversity branches increases, and we address the effects of diversity on coded modulation performance and design criteria, including the effect on interleaver depth (which affects the total delay of the system)     

Impact of diversity reception on fading channels with codedmodulation. II. Differential block detection

For pt. I see ibid., vol.45, no.6, p.563-572, 1997. We study coded modulation with block differential detection in an arbitrarily correlated Rician fading channel with space diversity. Coded differential q-PSK is included in our analysis as a special case. A metric is chosen that is optimum for perfect interleaving, slow fading, and independent diversity branches. For slow fading, we compare the the cutoff rates of the channels resulting from different choices of block length N and diversity index M. Specifically, we show that block detection with diversity may or may not generate a better coding channel than usual differential detection, according to the code selected and the combination of values of M and N. In particular, for low-diversity orders (M=1,2) and for low-to-medium code rates, differential detection is still an optimal or near-optimal solution, while for high-diversity orders (M⩾2) and medium-to-high code rates (up to uncoded modulation) block detection with N>2 can provide a significant gain. An error floor always exists when fading is fast. It decreases exponentially with the product of code diversity and space diversity, so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading. Performance examples based on actual coding schemes are also shown     

On diversity reception over fading channels with impulsive noise

In this paper, we analyze the performance of different diversity combining techniques over fading channels with impulsive noise. We use Middleton's Class A model for the noise distribution and adopt two noise models, which assume dependent and independent noise components on each branch. We systematically analyze the performance of maximum ratio combing (MRC), equal gain combining (EGC), selection combining (SC), and post-detection combining (PDC) under these impulsive noise models, and derive insightful lower and upper bounds. We show that even under impulsive noise, the diversity order is retained for each combining scheme. However, we also show that under both models, there is a fundamental tradeoff between diversity gain and coding gain. Under the independent noise model, PDC is shown to combat impulsive noise more effectively than MRC, EGC, and SC. Our simulation results also corroborate our analysis.     

Multistage interference cancellation with diversity reception forasynchronous QPSK DS/CDMA systems over multipath fading channels

This paper introduces a multistage interference cancellation (MIC) technique with diversity reception for quadrature phase shift keying (QPSK) asynchronous direct-sequence code division multiple access (DS/CDMA) systems over frequency-selective multipath Rayleigh fading channels. Unlike the previous MIC, which tries to remove the lump sum of the multiple-access interference (MAI) and self-interference (SI), this introduced MIC attempts to cancel only the MAI and part of the SI due to the intersymbol interference, while treating the remaining SI created by the current symbol as useful information for symbol decision. In this technique, the RAKE combining is used to collect signal replicas over multiple fading paths. Upper and lower bounds on the bit error probability are derived using a Gaussian approximation and the characteristic function method. Furthermore, effects of channel estimation error on the performance are studied. Analytical and simulation results show that the introduced MIC can provide a performance extremely close to that in an ideal single-user environment and outperforms the previous MIC even in the presence of channel estimation error     

Multichannel system with optimal diversity reception anderasures-correction decoder for Rayleigh fading channels

A multichannel (MC) system with optimal diversity reception and erasures correcting decoding of a block code applied to a Rayleigh fading channel is considered. The bit-error rate (BER) as a function of the signal-to-noise ratio has been found. It is shown that the proposed system has a lower BER than both the MC with forward-error correction and the MC with optimal uncoded diversity reception for the same redundancy     

Dual predetection SC diversity reception of TCM-MPSK signals overNakagami fading channels

Space diversity reception and forward error correction coding are powerful techniques for combatting multipath fading encountered in mobile radio communications. The authors analyse the performance of a dual predetection selection combining (SC) diversity system using trellis coded modulation-multiple phase shift keying (TCM-MPSK) on slow, nonselective correlated Nakagami fading channels. An alternative exact derivation for the pairwise error probability, used in calculating average bit error rate analytical upper bounds, is introduced     

Average probability of packet error with diversity reception over arbitrarily correlated fading channels

Closed form expressions for the average probability of packet error (PPE) are presented for no diversity, maximum ratio combining (MRC), selection combining (SC) and switch and stay combining (SSC) diversity schemes. The average PPE for the no diversity case is obtained in two alternative expressions assuming arbitrarily correlated Nakagami and Rician fading channels. For the MRC case, L diversity branches are considered and the channel samples are assumed to follow Nakagami distribution and to be arbitrarily correlated in both time and space. For the SC diversity scheme with L diversity branches, two bounds on the average PPE are derived for both slow and fast fading channels. The average PPE in this case is obtained in an infinite integral form for Nakagami channels while it is reduced to a closed form expression for the Rayleigh case. The average PPE is also derived in the case of SSC diversity with dual branches for both slow and fast Rayleigh fading channels. The new formulas are applicable for all modulation schemes where the conditional probability of error has an exponential dependence on the signal‐to‐noise ratio. The average PPE is then used to obtain a modified expression for the throughput for network protocols. In general, the diversity gain exhibits a little diminishing effect as the number of diversity branches increases. In addition, the system is found to be more sensitive to the space correlation than to the time correlation. The effects of different system parameters and diversity schemes are studied and discussed. Specific figures about the system performance are also provided. Copyright © 2004 John Wiley & Sons, Ltd.     

Combining PSA fading estimation techniques for TCM and diversity reception in Rician fading channels

In this paper, a novel pilot‐symbol‐aided (PSA) technique is proposed for fading estimation in the land mobile satellite fading channels. The proposed technique combines the fading estimates obtained from a bandwidth‐efficient technique and a conventional technique according to the signal‐to‐noise ratios (SNRs) of the fading estimates. To enhance the transmission quality, trellis‐coded modulation (TCM) and diversity reception are employed in the system, and the combined estimates are subsequently used to correct the channel fading effects, to weight the signals from different diversity branches, and to provide channel state information to the Viterbi decoder. Monte Carlo computer simulation has been used to study the bit‐error‐rate (BER) performance of the proposed technique on trellis‐coded 16‐ary quadrature amplitude modulation in the frequency non‐selective Rician fading channels. Results have shown that the proposed PSA technique requires a very low bandwidth redundancy to provide satisfactory BER performance at low SNRs, and thus is suitable for use with TCM and diversity reception to achieve both bandwidth and power‐efficient transmission. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive reception of MPSK on fading channels

An adaptive estimator of the complex gain of a fading channel is proposed. Tracking of the fading process is achieved without knowledge of the fading spectrum. This enables coherent detection of MPSK to be performed. Simulations show good error rate performance. The receiver finds applications in mobile radio communications     

Impact of channel-state information on coded transmission overfading channels with diversity reception

We study the synergy between coded modulation and antenna-diversity reception on channels affected by slow Rician fading. Specifically, we assess the impact of channel-state information (CSI) on error probability. We show that with a good coding and constant envelope modulations (for example, phase-shift keying) scheme the loss in performance when CSI is not available is moderate (around 1.5 dB). Moreover, as the diversity order grows, the channel tends to become Gaussian     

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.     

Error probability with incoherent diversity reception of FSKsignals transmitted over fast Rician fading channels

We compute the error performance of noncoherent detection receivers for FSK signals transmitted over fast frequency-flat Rician fading channels. Linearly time-varying fading models are used to derive closed-form expressions for the error probability of binary FSK signaling. Error bounds are established for the performance of M-ary orthogonal FSK. Simulation results are in excellent agreement with analytical predictions     

Co-channel interference analysis of shadowed Rician channels

This paper presents an exact analysis of co-channel interference (CCI) in a shadowed-Nakagami (desired)/shadowed-Rician (interfering) channel. Because a Rician distribution can be closely approximated by a Nakagami distribution (Nakagami 1960), the proposed analysis can be viewed as a close approximation of a shadowed-Rician (desired)/shadowed-Rician (interfering) model. The model provided in this paper includes many flexibilities-different Rice factors, different shadowing spreads, and different transmitted powers for desired and interfering signals. Therefore, it is a powerful tool for determining cell sizes and power levels in mixed micro/macro cellular systems     

Noncoherent MT-MFSK signals with diversity reception in arbitrarily correlated and unbalanced Nakagami-m fading channels

This paper studies the performance of diversity applied to an efficient modulation/coding scheme using M-ary frequency-shift keying (MFSK) signals, with postdetection noncoherent diversity reception and combining over slow nonselective arbitrarily correlated and unbalanced Nakagami-m fading channels, in which the diversity branches can have unequal signal-to-noise ratios (SNRs), as well as different severity parameter m. This modulation/coding scheme is referred to as multiple tone MFSK (MT-MFSK) and is implemented based on balanced incomplete block design (BIB-design) from combinatorial theory. In MT-MFSK modulation, the number of tones used to represent the signals set is reduced compared with the conventional MFSK modulation, and each MT-MFSK signal is represented by a number of distinct orthogonal tones selected according to BIB-design. This mechanism drastically increase the bandwidth efficiency of the modulated signal and allows the modulator to create implicit frequency diversity. In this paper, we show that by combining the implicit frequency diversity of MT-MFSK signals with the diversity reception introduced by employing multiple receiving antennas, substantial improvements in performance can be obtained. A noncoherent square-law combining (SLC) soft-decision receiver is introduced and a union bound expression for the average symbol error probability is obtained. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the unbalanced L diversity channels are considered. The system performance is compared with that of the conventional MFSK system. The results show that this modulation/coding scheme creates a multiplicative diversity and, therefore, performs better than the conventional MFSK system in terms of power and bandwidth efficiency.     

Comparison of decoding algorithms of binary linear block codes inRayleigh fading channels with diversity reception

The word error probability of binary linear block codes is evaluated in Rayleigh fading channels with diversity reception for three decoding algorithms: error correction (EC), error/erasure correction (EEC), and maximum likelihood (ML) soft decoding algorithms. The performance advantage of EEC over EC in the required average SNR decreases as the number of diversity channels increases. The performance advantage of EEC over EC does not depend on the specific value of word error probability although the advantage of ML soft decoding over EC increases for lower word error probability     

Performances of 16QAM with fading compensation and postdetection diversity reception in satellite mobile channels

This paper studies the effects of N-branch postdetection selection diversity reception, where N = 1, 2, 3 or 4, incorporated with fading compensation on a digital satellite mobile system. The digital satellite mobile system transmits a pilot-symbol-aided 16-ary quadrature-amplitude modulated (PSA-16QAM) signal over the Rician channels. A selection method that makes use of the pilot symbols to select one of the N branches in the diversity reception system for signal detection, and a novel PSA technique that makes use of both the pilot symbols and data symbols for fading compensation, are proposed. Computer simulation tests are used to assess the effects of the proposed techniques on bit-error rate performances (BER) of the PSA-16QAM system in the presence of additive white Gaussian noise (AWGN) or co-channel interference (CCI) in the Rician faded channels. When frequency diversity is used, PSA-16QAM with 2-branch and 4-branch diversity reception occupies about the same bandwidths as quaternary phase-shift-keying (QPSK) without using diversity and with 2-branch diversity, respectively, yet achieving the same capacity. Thus, simulation tests on the BER performances of a QPSK system without diversity and with 2-branch diversity are also carried out and the results are used to determine the preferred system arrangements. © 1997 John Wiley & Sons, Ltd.     

New selection diversity reception scheme effective for both frequency-flat and selective fading channels

A new selection diversity reception scheme is proposed, which combines and takes advantage of the maximum signal envelope branch selections (MEBS) and the minimum delay-spread branch selection (MDBS) schemes. The performance of the proposed scheme is theoretically investigated under frequency-flat and frequency-selective fading channel conditions and the improvement over the MEBS and the MDBS schemes is confirmed.<>     

Error rate analysis of MDPSK/CPSK with diversity reception undervery slow Rayleigh fading and cochannel interference

The distribution of the phase noise due to additive white Gaussian noise (AWGN) and cochannel interference (CCI) is analyzed for differential phase detection (DPD) and coherent phase detection (CPD) in a very slow nonfrequency selective Rayleigh fading environment. The effects of modulation timing offset between the desired signal and the CCI and of the overall channel filter response are considered. Simple closed-form expressions are derived for ideal selection diversity reception. The derived phase noise distributions are used for evaluating the bit error rate (BER) performance of 2-16DPSK/CPSK assuming square-root raised cosine Nyquist transmit/receive filters. It is found that the BER performance of CPSK is less sensitive to CCI modulation timing offset than DPSK, and that increasing the filter rolloff factor can improve the BER performance due to CCI. Finally, the accuracy of the BER approximation that uses the symbol error rate is discussed     

Error rates of M-ary signals with. Multichannel reception in Nakagami-m fading channels

In this letter, we present closed. form expressions for the exact average symbol-error rate (SER) of M-ary modulations with multichannel reception over Nakagami-m fading channels. The derived expressions extend already available results for the nondiversity case, to maximal-ratio combining-(MRC) and postdetection equal-gain combining (EGC) diversity systems. The average SERs are given in terms of Lauricella's multivariate hypergeometric function F/sub D//sup (n)/. This function exhibits a finite integral representation that can be used for fast and accurate numerical computation of the derived expressions.     

Exact symbol error probability of general order rectangular QAM with MRC diversity reception over nakagami-m fading channels

Exact average symbol error probability (SEP) of the general order rectangular quadrature amplitude modulation (QAM) with maximal ratio combining (MRC) diversity over L independent and identically distributed Nakagami-m fading channels with arbitrary fading index m is derived in this letter. The average SEP expression is given in terms of the Appell and Gauss hypergeometric functions and is then used to study the impact of diversity reception on the performance of general order rectangular QAM with different values of the quadrature-to-in-phase decision distance ratio. It is shown that the derived expression includes some existing results as special cases.