Performance Analysis of Multiple-Symbol Differential Detection based Space-Time Block Codes in Wireless Sensor Networks

It is well known that the performance of the wireless communication systems can be enhanced by using multiple transmit and receive antennas, which is generally referred to as the MIMO technique, and has been incorporated into the IEEE 802.11n standard, i.e. one of the Wi-Fi systems. The MIMO technique has also been adopted by the 3GPP Long Term Evolution (LTE) and the 3GPP2 Ultra Mobile Broadband (UMB) standards. The space-time coding is a promising way to realize the gain in the wireless communications system using MIMO. The space time block code, and the orthogonal space time block code in particular have been proposed in research and implemented in practical wireless communication systems due to their low computational complexity in maximum likelihood decoding implementation. However, the code rates of the orthogonal space time block codes are usually lower than $3/4$ when the number of transmit antennas is greater than two, which limit their throughput. To increase the code rate and the throughput of the orthogonal space time block code for more than two transmit antennas, a family of new space-time block codes (STBC) for 3 and 4 transmit antennas in a MIMO wireless communication system have been proposed in this Ph.D. research. These new codes are orthogonal and achieve full diversity, full rate using Triple QPSK'' modulation, which is proposed in this research. We investigated the performance of these STBCs when the channel state information (CSI) is perfectly known at the receiver. The CSI is not known to the transmitter in all of the studies in this dissertation. An analytical bound of the probability of bit error is developed and the Monte Carlo simulation is used when investigating these new STBC codes. In practical wireless communication system, the CSI is generally not available at the receiver and it is usually estimated by the receiver through the pilot signals or training signals known to the receiver. No matter what channel estimation method is used, the estimate of CSI will not match the CSI exactly and is noisy. The performance of these new STBCs using theTriple QPSK'' modulation when the estimate of the CSI is employed to detect the symbol is investigated in this dissertation. An upper bound of the bit error probability is developed when the noisy CSI is used to detect the symbols. The performance of the new STBCs using the Triple QPSK'' modulation is also evaluated using Monte Carlo simulation. When the CSI is not available to either the receiver or the transmitter, the differential encoding and decoding algorithm is applied to these new STBCs, which use theTriple QPSK'' modulation. The results showed that these orthogonal STBCs achieve full diversity full rate using ""Triple-QPSK"" modulation with differential detection. This provides a means of achieving space diversity and multiplexing gain without the CSI. A new differential encoding and decoding algorithm is proposed and analyzed for STBCs with 3 transmit antennas, whose transmission matrix is not square matrix, as part of this Ph.D. research. The STBCs using this algorithm achieve full diversity the MIMO system can possibly provide.

Approximately 3 dB signal-to-noise ratio (SNR) loss is always paid with conventional differential space-time block codes (STBCs), compared with coherent STBCs. In this paper, a multiple-symbol differential detection (MSDD) technique is proposed for M-ary phase-shift keying (PSK) STBCs. The new scheme can greatly narrow the 3-dB performance gap by extending the observation interval for differential decoding. The technique uses maximum-likelihood sequence detection instead of traditional symbol-by-symbol detection, and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric is derived for an observation interval of arbitrary length. It is shown that for a moderate number of symbols, MSDD provides approximately 1.5 dB performance improvement over conventional differential detection. In addition, a closed-form pairwise error probability and approximate bit-error probability (BEP) are derived for multiple-symbol differential binary PSK STBC. Results show that the theoretical BEP matches simulation results well. The BEP is shown to converge asymptotically with the number of symbols in the observation interval to that of the differential scheme with coherent detection.

In distributed space-time coding cooperative systems, differential detection gains much attention because it needs no channel state information at the receivers. But conventional differential detection performs about 3dB loss than coherent detection. In this paper, we propose a multiple-symbol differential detection algorithm for relay networks based on maximum-likelihood principle. The simulation results show that the multiple-symbol differential detection can narrow the performance gap between the conventional differential detection and coherent detection for Alamouti and square real orthogonal coding systems with corresponding numbers of relays, especially in high signal-tonoise ratio regime. And with the increase of observation window size, the Doppler effect on performance is decreased and the error floor encountered in conventional differential detection can be eliminated provided that the value of observation window size is sufficiently high.

A new MIMO transceiver is proposed for the downlink of high data rate multicarrier CDMA (MC-CDMA) systems over frequency-selective multipath channels. The design of the transceiver involves the following procedure. First, the data stream is demultiplexed into multiple substreams, which are then encoded by a set of space time block codes (STBC) for achieving spatial diversity. Second, the coded substreams are spread by a set of space-path spreading (SPS) codes which is designed to achieve path multiplexing by exploiting independent multipath channels and pre-suppress the multiple access interference (MAI) without the use of channel state information (CSI). These substreams are then transmitted simultaneously from multiple antennas. At each mobile station, a simple matched filter (MF) is used to despread the received data. Linearly combining the MF outputs with the aid of CSI and employing a multi-user detection scheme can then separate the mutually interfering signals from the multiple transmit antennas and restore the diversity gain due to SPS and STBC. An increased spectral efficiency and diversity gain can thus be achieved at the same time. Simulation results confirm that the proposed transceiver offers better performance than the conventional BLAST transceiver, and achieves nearly the performance of STBC and space-time spreading BLAST transceiver.

In this letter, an orthogonal space-time (ST) block coding (STBC) technique for continuous phase modulation (CPM) is proposed and combined with a frequency domain equalizer (FDE) to obtain high performance gains over frequency-selective channels. The new method maintains the constant envelope and phase continuity of the CPM waveforms perfectly by using appropriate tail symbols during the addition of cyclic prefix and interblock transitions and, therefore, has no negative impact on the spectral efficiency. Because the STcoded CPM blocks remain orthogonal, FDE is applied as in the case of single antenna transmissions without any increase in the computational load. Simulations corroborate the performance improvement offered by STBC while also preserving the desired bandwidth efficiency of CPM.

Space-time block code (STBC) based on orthogonal design is one of the space-time coding methods to achieve multi-input multi-output (MIMO) diversity gain. STBC can provide sufficient space diversity gain, but it can not provide coding gain. Polar codes based on channel polarization are the first class of provably capacity-achieving codes with low encoding and decoding complexity. In order to improve the bit error rate (BER) performance of STBC, a concatenated scheme with Polar codes and STBC, named Polar-STBC scheme, is proposed in this paper. The BER performance of Polar-STBC system is discussed by numerical simulation under different polar code length, different polar code rates, and different coding methods of STBC. The results show that the performance of Polar-STBC has a big improvement in comparison with that using STBC only. The coding gain of Polar-STBC system is about 5dB when the BER is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . Meanwhile, the longer code length and the lower code rate Polar codes have, the better BER performance the Polar-STBC system has. In addition, the different STBC coding methods have influence on the Polar-STBC system. The Polar-STBC system with more receiving antennas has a better BER performance in comparison with those with the same sending antennas and less receiving antennas. The coding gain of Polar-STBC system with 2 receiving antenna is 6.5dB improvement to the system with 1 receiving antenna when BER is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and the code length is 1024.

Orthogonal space-time block codes (STBC) constitute a simple way of exploiting transmit diversity. If no channel knowledge is available at the transmitter the use of diversity can increase performance significantly. However, if some partial channel state information (CSI) is available, such as knowledge of the transmit correlation matrix, adapting transmission to this knowledge provides additional performance gains. In such case, adaptivity can be introduced by using a unitary eigenbeamformer with beams pointing along the directions of the eigenvectors of the transmit correlation matrix and applying a convenient power loading along the resulting beams. While for Rayleigh-fading channel eigenbeamforming has been shown to be optimum in terms of ergodic capacity, so far, no closed solution for the optimum power loading has been found. In the work at hand, orthogonal STBC are combined with eigenbeamforming in an orthogonal frequency-division multiplexing (OFDM) context and an optimum power loading is found, where optimality refers to an upperbound of pairwise error probability (PEP). The resulting signaling scheme can be viewed as an extension of STBC to OFDM with partial channel knowledge. The solution represents a very interesting trade-off between transmit diversity and antenna gain.

We consider multiple?symbol differential detection (MSDD) for multiple?input multiple?output Rayleigh?fading channels. MSDD, which jointly processes blocks of received symbols to detect N -1 data symbols, allows for power?efficient transmission without requiring channel state information at the receiver. In previous work, we showed that computationally efficient sphere decoding algorithms can be used to accomplish MSDD. In this paper, we analyze the computational complexity of this sphere?decoding based MSDD. In particular, we prove by means of a lower bound that the complexity of the Fincke?Pohst multiple?symbol differential sphere decoder (FP?MSDSD), while being very low over wide ranges of N and signal?to?noise ratios, is exponential in N in principle. We further derive expressions for the exact complexity of FP?MSDSD, which allow for quick assessment of ranges of useful window sizes N.

The conventional multiple-symbol differential detection (MSDD) of differential phase-shift keying (DPSK) signals is studied in the presence of frequency offset. It is shown that in the case of nonzero frequency offset, the performance of the conventional MSDD receiver degrades by increasing the number of observed samples. A double DPSK (DDPSK) modulation scheme is then introduced and it is shown that in the presence of nonzero frequency offset, an MSDD receiver with DDPSK modulation outperforms a conventional MSDD receiver with DPSK modulation, when both receivers use a large number of received samples. Examples lead to a conjecture that the performance of an optimum MSDD receiver with DDPSK modulation and an infinite number of received samples, approaches that of a conventional DPSK demodulator with two received samples.

Large MIMO systems with tens of antennas in each communication terminal using full-rate non-orthogonal space- time block codes (STBC) from cyclic division algebras (CDA) can achieve the benefits of both transmit diversity as well as high spectral efficiencies. Maximum-likelihood (ML) or near-ML decoding of these large-sized STBCs at low complexities, however, has been a challenge. In this paper, we establish that near-ML decoding of these large STBCs is possible at practically affordable low complexities. We show that the likelihood ascent search (LAS) detector, reported earlier by us for V-BLAST, is able to achieve near-ML uncoded BER performance in decoding a 32 times 32 STBC from CDA, which employs 32 transmit antennas and sends 32 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 1024 complex data symbols in 32 time slots in one STBC matrix (i.e., 32 data symbols sent per channel use). In terms of coded BER, with a 16 times 16 STBC, rate-3/4 turbo code and 4-QAM (i.e., 24 bps/Hz), the LAS detector performs close to within just about 4 dB from the theoretical MIMO capacity. Our results further show that, with LAS detection, information lossless (ILL) STBCs perform almost as good as full-diversity ILL (FD-ILL) STBCs. Such low-complexity detectors can potentially enable implementation of high spectral efficiency large MIMO systems that could be considered in wireless standards.

Multiple-symbol differential detection (MSDD) for multiple-input-multiple-output Rayleigh-fading channels is considered. MSDD, which jointly processes blocks of N received symbols to detect N-1 data symbols, allows for power-efficient transmission without requiring channel state information at the receiver. In previous work, the authors showed that computational efficient sphere decoding algorithms can be used to accomplish MSDD. In this correspondence, the computational complexity of this sphere-decoding based MSDD is analyzed. In particular, it is proven by means of a lower bound that the complexity of the Fincke-Pohst multiple-symbol differential sphere decoder (FP-MSDSD), while being very low over wide ranges of N and signal-to-noise ratios, is exponential in N in principle. Furthermore, both exact and simple approximate expressions for the complexity of FP-MSDSD are derived, which allow for quick assessment of ranges of useful window sizes N of FP-MSDSD and show that the exponential rate of growth of the complexity of FP-MSDSD is asymptotically equal to that of brute-force MSDD

In this paper, we propose a novel multiple symbol differential detection (MSDD) based on symbol error position estimation (SEPE) and compensation for use in terrestrial digital multimedia broadcasting (T-DMB) system. By estimating the symbol error position and compensating for the symbol error using MSDD outputs, it can improve the receive performance of T-DMB system. Also by providing soft-outputs to Viterbi decoder, an additional coding gain can be obtained. Simulation results in the typical urban (TU) channel show that the proposed algorithm is superior to the conventional differential detection (DD) and hard decision based MSDD T-DMB receivers.

In this paper, multiple-symbol differential detection (MSDD) is applied to the differential single-carrier frequency-division multiple access (SC-FDMA) system. Both time domain and frequency domain MSDD are investigated to compensate for the performance loss of conventional differential detection comparing with coherent detection. The decision metric of time and frequency domain MSDD for SC-FDMA are derived respectively. Simulation results demonstrate the effectiveness of MSDD in some situations.

The space-time coding can provide a diversity gain for the multiple-antenna system while spatial multiplexing provides higher data rates. In this paper we are combining space-time block code (STBC) with spatial multiplexing technique over space to take advantages of both schemes. The transmit antennas are divided into groups, with one of the groups transmitting STBC code given by Alamouti and other transmits spatial multiplexing data. At the receiver, a minimum mean square error (MMSE) detector with interference cancelation (IC) is integrated with the space-time decoder to reconstruct the desired signal effectively. MMSE decoder is used for compared to only MMSE method. STBC coded symbols (estimation of interfering terms and then space-time decoder is applied. 4×1 system gives slightly higher diversity gain with rate=3 as s1s2) are giving 8 dB gain as compared to purely orthogonal code (2×1 MMSE-SIC). Rate of 3×1 system is less but it is performing better in terms of reliability as compared to 4×1 system.

Multiple-symbol differential detection (MSDD) is a promising technique to enhance the performance of ultra-wideband (UWB) communications without estimating the channel explicitly. In this context, the generalized log-likelihood ratio test (GLRT) for MSDD was developed, and the hard-output multiple-symbol detector was proposed, which exhibits considerable bit-error-rate (BER) performance improvement over transmitted reference transmissions. In this paper, we further improve the system performance by incorporating error correction code (ECC) and iterative processing at the receiver. The soft-input soft-output (SISO) MSDD is developed to deliver a posteriori information to the outer ECC decoder and enables iterative detection and decoding. Simulations show that the iterative processing achieves significant gains over the existing MSDD in UWB communications.