M-ary phase coding for the noncoherent AWGN channel

This work considers coded M-ary phase-shift keying (MPSK) schemes with noncoherent detection. A class of block codes called module-phase codes is described. The algebraic framework used for describing these codes relies on elements from module theory which are discussed along with a method for constructing such codes for noncoherent detection. It is shown that differential encoding may be viewed as a specific code from a particular class of module-phase codes. Two classes of codes that achieve significant coding gain with respect to coherent detection of uncoded MPSK are presented. In the first class of module-phase codes, the coding gain is achieved at the expense of bandwidth expansion. In the second class, however, the coding gain is achieved at the expense of signal constellation expansion without expanding bandwidth. Finally, an integrated demodulation/decoding technique based on a modification of information set decoding is presented. It Is shown that this reduced-complexity, suboptimal decoding strategy performs nearly as well as maximum-likelihood decoding     

Capacity of blockwise noncoherent M-APSK/AWGN channel

Capacity-achieving input distribution for the blockwise noncoherent M-APSK/AWGN channel is characterised. Upper and lower bounds on the normalised capacity, with and without the use of differential encoding, are derived. They show that the coherent channel capacity is approached with increasing channel coherence interval. Moreover, they indicate that the coherent capacity is approximated faster with differential encoding.     

Rotationally invariant and rotationally robust codes for the AWGN and the noncoherent channel

The paper investigates the design and robustness of rotationally invariant (RI) codes. First, RI codes are extended to the case of serially concatenated (SC) trellis-coded modulation (TCM) and several high-rate powerful RI-SCTCM codes are designed over 8-phase-shift keying and 16-quadrature amplitude modulation alphabets. The investigation continues by considering more realistic channels that introduce cycle slips during phase estimation, and thus rotate only part of the transmitted codeword. It is proven that RI codes with small state space are robust in these channels, even when traditional coherent decoders are utilized. Furthermore, it is demonstrated through simulations that the addition of a simple stopping criterion to the coherent iterative decoding algorithm is sufficient for robustness of the more powerful RI-SCTCM codes when partial codeword rotations are considered. Finally, it is investigated whether RI codes are useful for transmission in the noncoherent channel. It is proved that RI codes are as good as any other good codes for this channel when the phase dynamics are low, and optimal decoding is performed. However, it is shown that for a certain class of receivers, RI codes are also robust to partial phase rotations in this channel.     

On coding without restrictions for the AWGN channel

Many coded modulation constructions, such as lattice codes, are visualized as restricted subsets of an infinite constellation (IC) of points in the n-dimensional Euclidean space. The author regards an IC as a code without restrictions employed for the AWGN channel. For an IC the concept of coding rate is meaningless and the author uses, instead of coding rate, the normalized logarithmic density (NLD). The maximum value C_∞ such that, for any NLD less than C_∞, it is possible to construct an PC with arbitrarily small decoding error probability, is called the generalized capacity of the AWGN channel without restrictions. The author derives exponential upper and lower bounds for the decoding error probability of an IC, expressed in terms of the NLD. The upper bound is obtained by means of a random coding method and it is very similar to the usual random coding bound for the AWGN channel. The exponents of these upper and lower bounds coincide for high values of the NLD, thereby enabling derivation of the generalized capacity of the AWGN channel without restrictions. It is also shown that the exponent of the random coding bound can be attained by linear ICs (lattices), implying that lattices play the same role with respect to the AWGN channel as linear-codes do with respect to a discrete symmetric channel     

Signal design and convolutional coding for noncoherent space-timecommunication on the block-Rayleigh-fading channel

We consider the problem of designing signal constellations for the multiple transmit-multiple receive antenna Rayleigh-fading communication channel, when neither the transmitter nor the receiver know the fading. In particular, by employing the asymptotic union bound (AUB) on the probability of error, we give a new formulation of the problem of signal design for the noncoherent fading channel. Since unitary signals are optimal for this channel (in the limit of large signal-to-noise ratios SNRs), the problem can be posed in terms of packings on the Grassmanian manifold. A key difference in our approach from that of other authors is that we use a notion of distance on this manifold that is suggested by the union bound. As a consequence of our use of this distance measure, we obtain signal designs that are guaranteed to achieve the full diversity order of the channel, a result that does not hold when the chordal distance is used. We introduce a new method of recursively designing signals, termed successive updates, to approximately optimize this performance measure. We then examine the use of our signals with several convolutional codes over the fading channel. An upper bound on the bit error probability of the maximum-likelihood decoder is presented together with an asymptotic analysis of that bound     

ARO scheme with combined channel coding and modulation using noncoherent detection

A new method for the combination of channel coding and modulation with noncoherent detection in automatic-repeat-request protocols is described. This scheme can be used in automatic-repeat-request protocols in which each codeword is transmitted m >or= 2 times consecutively. Theoretical analysis shows that this scheme offers a net increase in the performance with respect to other similar protocols.<>     

Capacity of time-slotted ALOHA packetized multiple-access systems over the AWGN channel

We study different notions of capacity for time-slotted ALOHA systems. In these systems, multiple users synchronously send packets in a bursty manner over a common additive white Gaussian noise (AWGN) channel. The users do not coordinate their transmissions, which may collide at the receiver. For such a system, we define both single-slot capacity and multiple-slot capacity. We then construct a coding and decoding scheme for single-slot capacity that achieves any rate within this capacity region. This coding and decoding scheme for a single time slot combines aspects of multiple access rate splitting and of broadcast codes for degraded AWGN channels. This design allows some bits to be reliably received even when collisions occur and more bits to be reliably received in the absence of collisions. The exact number of bits reliably received under both of these scenarios is part of the code design process, which we optimize to maximize the expected rate in each slot. Next, we examine the behavior of the system asymptotically over multiple slots. We show that there exist coding and decoding strategies such that regardless of the burstiness of the traffic, the system is stable as long as the average rate of the users is within the multiple access capacity region of the channel. In other words, we show that bursty traffic does not decrease the Cover-Wyner capacity region of the multiple access channel. A vast family of codes, which includes the type of codes we introduce for the single-slot transmission, achieve the capacity region, in a sense we define, for multiple-slot transmissions. These codes are stabilizing, using only local information at each of the individual queues. The use of information regarding other queues or the use of scheduling does not improve the multiple-slot capacity region.     

On the capacity-achieving distribution of the discrete-time noncoherent and partially coherent AWGN channels

We investigate the communication limits over rapid phase-varying channels and consider the capacity of a discrete- time noncoherent additive white Gaussian noise (NCAWGN) channel under the average power constraint. We obtain necessary and sufficient conditions for the capacity-achieving input distribution and show that this distribution is discrete and possesses an infinite number of mass points. Using this characterization of the capacity-achieving distribution we compute a tight lower bound on the capacity of the channel based on examining suboptimal input distributions. In addition, we provide some easily computable lower and upper bounds on the channel capacity. Finally, we extend some of these results to the partially coherent channel, where it is assumed that a phase-locked loop (PLL) is used to track the carrier phase at the receiver, and that an ideal interleaver and de-interleaver are employed-rendering the Tikhonov distributed residual phase errors statistically independent from one symbol interval to another.     

Code and receiver design for the noncoherent fast-fading channel

This paper deals with the design of coding/modulation and demodulation/decoding schemes for single- or multiple-antenna systems with focus on fast-fading channels, where channel state information (CSI) is not available at the transmitter and the receiver. We explore two possible solutions for this channel with increasing degree of sophistication. The first one utilizes pilots at the transmitter and a simple and explicit noniterative channel estimation algorithm at the receiver. We show that this pilot-assisted system is exactly equivalent, in terms of performance analysis and design, to an appropriately "degraded" system having perfect CSI at the receiver. The second scheme utilizes pilots and a family of well-justified and simple suboptimal iterative detection/estimation algorithms. It is shown that when turbo-like codes are considered in conjunction with this pilot-assisted transmission scheme and the proposed receiver algorithm, the unitary constellations investigated in the literature are inferior to simple pilot-assisted constellations in both complexity and performance. Specific instances of the proposed systems (that use optimized irregular low-density parity-check outer codes) are designed. The design examples provided show that the proposed systems can achieve a good tradeoff between complexity and performance and can be used to bridge the gap between the high complexity/high-performance optimal scheme and low-complexity/mediocre performance noniterative estimation/coherent detection scheme.     

A comparison of SNR estimation techniques for the AWGN channel

The performances of several signal-to noise ratio (SNR) estimation techniques reported in the literature are compared to identify the "best" estimator. The SNR estimators are investigated by the computer simulation of baseband binary phase-shift keying (PSK) signals in real additive white Gaussian noise (AWGN) and baseband 8-PSK signals in complex AWGN. The mean square error is used as a measure of performance. In addition to comparing the relative performances, the absolute levels of performance are also established; the simulated performances are compared to a published Cramer-Rao bound (CRB) for real AWGN and a CRB for complex AWGN that is derived here. Some known estimator structures are modified to perform better on the channel of interest. Estimator structures for both real and complex channels are examined.     

Energy efficient communications over the AWGN relay channel

This paper addresses the energy efficiency analysis of the relay channel under additive white Gaussian noise. We consider the rate bounds given by decode and forward and the cut set bound and assume that resources are optimally allocated to maximize the spectral efficiency according to the channel information and the sum network energy. The low energy analysis tools are used to compute the maximum rate per energy (RPE) and the slope of the spectral efficiency as a function of the energy per bit. Using these metrics, the energy efficiency benefit of several capabilities at terminals is investigated. Specifically, we take into account: i) the phase synchronization between transmitters, ii) the full duplex capability at the relay and iii) the channel access via superposition.     

AWGN信道下PSK信号幅度与信噪比的估计

研究了AWGN信道下PSK信号幅度和信噪比的估计问题，提出了一种基于迭代的直接判决反馈估计算法，并对其性能进行了分析和仿真。仿真结果表明：低信噪比下经过多次迭代后，由于误码导致的估计偏差可得到较大程度的补偿，估计器的性能接近有数据辅助时的性能，明显优于直接判决反馈时的性能。     

On the complexity of bounded distance decoding for the AWGN channel

Earlier work has derived the storage complexity of the bounded distance decoder (BDD) for binary channel convolutional codes. We extend this work to the Gaussian noise channel and to partial-response codes. We show that the storage requirement ~(2^1-R - 1)^-t paths for rate-R convolutional codes over the binary channel becomes ~2 ^2Rt over the Gaussian channel, where the decoder must correct t errors. Thus, convolutional coding over the Gaussian channel is not only 3 dB more energy efficient, but its decoding is simpler as well. Next, we estimate the path storage for partial-response codes, i.e., real-number convolutional codes, over the Gaussian channel. The growth rate depends primarily on the bandwidth of the code. A new optimization procedure is devised to measure the maximum storage requirement in Gaussian noise for these two code types. An analysis based on difference equations predicts the asymptotic storage growth for partial response codes     

Capacity of cellular dynamic channel assignment schemes employingadaptive modulation and coding

An investigation into the benefits of introducing adaptive modulation and coding techniques into a cellular system employing dynamic channel assignment is performed for the case of a fixed wireless access network conveying fixed-bandwidth information. It is shown that in the typical cases considered, the introduction of adaptive modulation and coding can actually reduce the capacity of the system     

Pilot-symbol-assisted coded transmission over the block-noncoherent AWGN channel

In this paper, pilot-symbol-assisted transmission in conjunction with high-performance coding over the block-independent noncoherent additive white Gaussian noise channel is investigated. Several approximate iterative receivers are proposed, which either perform carrier-phase estimation separately from detection, or joint carrier-phase estimation/decoding in an iterative fashion. The performance of the proposed receivers is analyzed using density evolution. The power allocation to the pilot symbol is quantified, and it is shown that an optimal allocation scheme exists that minimizes the overall information bit signal-to-noise ratio required for error-free communication. This optimal power allocation, which could be utilized in code design, is found to be sensitive to the channel coherence interval, as well as to the particular receiver used. In addition, a simple upper bound on the performance of any receiver that performs joint iterative carrier-phase estimation and detection, is derived. The obtained results are compared with the simulated performance of the proposed receivers.     

Capacity and coding for the Gilbert-Elliot channels

The Gilbert-Elliott channel, a varying binary symmetric channel, with crossover probabilities determined by a binary-state Markov process, is treated. In general, such a channel has a memory that depends on the transition probabilities between the states. A method of calculating the capacity of this channel is introduced and applied to several examples, and the question of coding is addressed. In the conventional usage of varying channels, a code suitable for memoryless channels is used in conjunction with an interleaver, with the decoder considering the deinterleaved symbol stream as the output of a derived memoryless channel. The transmission rate is limited by the capacity of this memoryless channel, which is often considerably less than the capacity of the original channel. A decision-feedback decoding algorithm that completely recovers this capacity loss is introduced. It is shown that the performance of a system incorporating such an algorithm is determined by an equivalent genie-aided channel, the capacity of which equals that of the original channel. The calculated random coding exponent of the genie-aided channel indicates a considerable increase in the cutoff rate over that of the conventionally derived memoryless channel     

Lattice codes can achieve capacity on the AWGN channel

It is shown that lattice codes can achieve capacity on the additive white Gaussian noise channel. More precisely, for any rate R less than capacity and e>0, there exists a lattice code with rate no less than R and average error probability upper-bounded by e. These lattice codes include all points of the (translated) lattice within the spherical bounding region (not just the ones inside a thin spherical shell)     

Iterative decoding and channel estimation for space-time BICM over MIMO block fading multipath AWGN channel

In this paper, we consider a generic model of space-time bit-interleaved coded modulation (ST-BICM) on a multiple-input multiple-output (MIMO) Rayleigh fading multipath channel. A practical low-complexity receiver structure performing iteratively MIMO data detection, channel decoding and channel estimation, is presented. The MIMO data detection, employing a reduced-state list-type soft output Viterbi algorithm enables to cope with severe channel intersymbol interference (ISI) without MIMO prefiltering. Among other results, simulations show that our approach can dramatically improve the downlink performance of time-division multiple access (TDMA) systems with high order modulation, keeping a reasonable complexity at the receiver side.     

基于数据辅助的AWGN信道下QPSK信号信噪比估计

提出了一种以噪声功率为主导的新的信噪比估计算法,仿真结果表明,该算法比现有的基于DA的最大似然估计方法具有更好的性能,尤其在低信噪比条件下,可以同时具有更好的精度和更高的可信度,而且不受接收机相位误差的影响.最后分析了本算法的误差来源,并给出了应用建议.