Annavajjala Ramesh

BER analysis of QAM with transmit diversity in Rayleigh fading channels

In this paper, we present a log-likelihood ratio (LLR) based approach to analyze the bit error rate (BER) performance of quadrature amplitude modulation (QAM) on Rayleigh fading channels without and with transmit diversity. We derive LLRs for the individual bits forming a QAM symbol both on flat fading channels without diversity as well as on channels with transmit diversity using two transmit antennas (Alamoutis scheme) and multiple receive antennas. Using the LLRs of the individual bits forming the QAM symbol, we derive expressions for the probability of error for various bits in the QAM symbol, and hence the average BER. In addition to being used in the BER analysis, the LLRs derived can be used as soft inputs to decoders for various coded QAM schemes including turbo coded QAM with transmit diversity, as in high speed downlink packet access (HSDPA) in 3G.

Performance of noncoherent turbo detection on Rayleigh fading channels

We are concerned with the performance of turbo codes on Rayleigh fading channels when noncoherent detection is employed. Performance of turbo codes with noncoherent detection on AWGN channels has been analyzed by E.K. Hall and S.G. Wilson (see Proc. IEEE Commun. Theory Mini-Conf, p.66-70, 1997). They compared the performance of turbo codes with the achievable information theoretic channel capacity for noncoherent detection on AWGN channels. We derive the information theoretic channel capacity for noncoherent detection on Rayleigh fading channels, and show that the noncoherent turbo decoder achieves performance close to this theoretical capacity (within 1.5 dB). We further show that the performance of noncoherent turbo decoder without the knowledge of channel fades is quite close (within 0.5 dB at 10/sup -5/ BER) to that with perfect knowledge of the channel fades. Optimum decoding of turbo codes requires the knowledge of channel SNR. With this requirement in mind, we propose online SNR estimation schemes, based on the ratio of certain observables at the output of the noncoherent detector, which when used in the turbo decoder gives performance very close to that with perfect knowledge of channel SNR.

A first-order Markov model for correlated Nakagami-m fading channels

We propose a first-order Markov model for generalized Nakagami-m (1960) flat fading channels. Using a moment generating function (MGF) approach, we derive the parameters of the proposed model for any value of the fading severity index m /spl ges/ 0.5. The proposed model is a generalized version of the one proposed earlier by Zorzi et al. (1995) for flat Rayleigh fading channels. For m = 1, we show that our generalized model gives the same parameter values obtained using Zorzis approach. Our generalized model thus encompasses Zorzis model as a special case. We illustrate the usefulness of our proposed Markov model by applying it to the analysis of the throughput and energy efficiency performance of a link layer (LL) protocol with backoff on wireless fading links with different values of the m-parameter (= 0.5,1,4).

Bounds on the performance of turbo codes on Nakagami fading channels with diversity combining

We derive bit error performance bounds for turbo codes on Nakagami fading channels with diversity combining. We first derive the average pairwise error probability expressions for turbo codes with maximal ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) on Nakagami fading channels. Using the pairwise error probability expressions and the union bounding technique, we then obtain bounds on the bit error probability of turbo codes for MRC, EGC, and SC diversity schemes. We present the modified log-MAP turbo decoder for MRC, EGC, and SC, and compare the analytical bounds with simulation results for the special case of 2-antenna diversity with Nakagami parameter m=1 (i.e., Rayleigh fading). Results indicate that the EGC scheme with turbo coding performs close to MRC scheme for i.i.d Rayleigh fading.

LLR based BER analysis of orthogonal STBCs using QAM on Rayleigh fading channels

We derive analytical expressions for the bit error rate (BER) of space-time block codes (STBC) from complex orthogonal designs (COD) with quadrature amplitude modulation (QAM) on Rayleigh fading channels. We take a bit log-likelihood ratio (LLR) based approach to derive the BER expressions. We first derive the LLRs for the various bits forming the QAM symbol and use these LLRs to derive analytical expressions for the error rate of the individual bits forming the QAM symbol and hence the average BER of the system. The approach presented in this paper can be used in the BER analysis of any STBC from COD with linear processing, for any value of M in a 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. 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.

SNR estimation in Nakagami fading with diversity for turbo decoding

In this paper, we propose an online SNR estimation scheme for Nakagami-m fading channels with equal gain diversity combining. We derive the SNR estimates based on the statistical ratio of certain observables over a block of received data. An online SNR estimator for an AWGN channel has been derived by Summers and Wilson (1998). Previously, we derived an SNR estimation scheme for Nakagami-m fading channels without diversity combining and used this estimate in the decoding of turbo codes. Now, we extend the work and solve the SNR estimation problem on Nakagami fading channels with L-branch equal gain diversity combining. We use our SNR estimates in the iterative decoding of turbo codes on Rayleigh fading channels (m=1) with 2-branch equal gain combining. We show that the turbo decoder performance using our SNR estimates is quite close (within 0.5 dB) to the performance using perfect knowledge of the SNR and the fade amplitudes.

Performance analysis of generalized selection combining of M-ary NCFSK signals in Rayleigh fading channels

In this paper, we propose and analyze the bit error performance of a generalized selection combining (GSC) receiver for M-ary non-coherent frequency shift keying (NCFSK) signals on i.i.d. Rayleigh fading channels with L antennas at the receiver. For each of the M hypotheses, the receiver combines the K largest outputs among the L available square-law detector outputs before proceeding to the bit detection process. We derive a closed-form expression for the bit error probability of the proposed (K, L) GSC receiver, and present numerical results to illustrate the bit error performance of this receiver for different values of M, K, and L. We also show that our generalized (K, L) GSC scheme and analysis encompass the previously reported schemes/analyses by Chyi et al. and Hahn a special cases for K = 1 and K = L, respectively.

Performance analysis of TCM with generalized selection combining on Rayleigh fading channels

We derive the computational cutoff rate, R/sub 0/, for coherent trellis-coded modulation (TCM) schemes on independent identically distributed (i.i.d.) Rayleigh fading channels with (K, L) generalized selection combining (GSC) diversity, which combines the K paths with the largest instantaneous signal-to-noise ratios (SNR) among the L available diversity paths. The cutoff rate is shown to be a simple function of the moment generating function (MGF) of the SNR at the output of the (K, L) GSC receiver. We also derive the union bound on the bit error probability of TCM schemes with (K, L) GSC in the form of a simple, finite integral. The effectiveness of this bound is verified through simulations.

Optimum selection combining of binary NCFSK signals on independent Rayleigh fading channels

In this paper, we derive a new selection combining (SC) scheme for noncoherent binary FSK signals on independent (but not necessarily identically distributed) Rayleigh fading channels with L-antenna diversity reception. With this combining scheme, we choose the diversity branch having the largest magnitude of the logarithm of the ratio of the a posteriori probabilities (log-APP ratio - LAPPR) of the transmitted information bit. We show that this scheme minimizes the probability of bit error, thus proving the optimality. We also show that a) the traditional square-law combining of all L diversity branches is equivalent to combining the LAPPR of all the L diversity branches, and b) the SC scheme proposed by Neasmith and Beaulieu (1998) is a special case of the proposed optimum SC scheme for independent and identically distributed (i.i.d) Rayleigh fading. Bit error probability results show that, at 10/sup -4/ BER, a) for i.i.d Rayleigh fading, the proposed optimum SC combining scheme performs better than the existing SC schemes by 0.5 dB for L = 3 and 1.5 dB for L = 5, and performs within 0.5 dB of the scheme which square-law combines all the L diversity branches, and b) for independent Rayleigh fading, the proposed optimum SC scheme gives an additional gain of 2.0 dB over the SC schemes of Pierce (1958) and Chyi et al. (1989).

Performance analysis of a (3, L) selection combining scheme for binary NCFSK signals on Rayleigh fading channels

In a previous paper, we derived the optimum selection combining (OSC) scheme for binary noncoherent FSK (NCFSK) signals on independent (but not necessarily identically distributed) Rayleigh fading channels with L-antenna diversity reception. In the OSC scheme, the diversity branch having the largest magnitude of the logarithm of the ratio of the a posteriori probabilities (log-APP ratio - LAPPR) of the transmitted information bit is chosen. In this paper, we derive the bit error performance of a (3, L) selection combining scheme for binary NCFSK signals which combines the three branches whose LAPPR magnitudes are the largest among the available L branches in i.i.d Rayleigh fading. Numerical results for this (3, L) selection scheme show that, for L=5, combining the three branches with the largest LAPPR magnitudes yields almost the full performance of the square-law combining of all the L=5 branches. For L=7, the performance of combining the three branches with the largest LAPPR magnitudes is just about 0.2 dB worse from the performance of square-law combining of all the L=7 branches. We also compare the performance of the proposed (3, L) selection scheme with the (3, L) selection combining scheme of Chyi et al. (1989).