Single-path Channel Model Research Articles

Training Beam Sequence Design for Multiuser Millimeter Wave Tracking Systems

In this paper, a novel training beam sequence design for multiuser millimeter wave tracking systems is proposed. For each receiver, a single-path channel model is firstly investigated, where we introduce a maximum a posteriori (MAP) criterion to estimate the time-varying angle of departure (AoD), followed by an extended Kalman filter to update the stale complex path gain. We then employ training beam sequence design to minimize the estimated AoD’s average mean squared error (AMSE), which however has no explicit expression. We firstly derive a closed-form upper bound for the AMSE and then simplify this upper bound into a tractable form, based on which a nonlinear optimization problem (NLP) is formulated. By solving this NLP optimally using its corresponding Karush-Kuhn-Tucker conditions, we obtain an efficient training beam sequence. The proposed MAP criterion and its associated training beam sequence design are further extended to multi-path scenarios, where a joint estimation of the multiple paths is firstly discussed, followed by a sequential estimation as a low-complexity alternative. Numerical results demonstrate the superiority of our proposed scheme over the existing benchmark methods, especially in the case when the receivers’ channels change rapidly.

Active Learning and CSI Acquisition for mmWave Initial Alignment

Millimeter wave (mmWave) communication with large antenna arrays is a promising technique to enable extremely high data rates due to the large available bandwidth in mmWave frequency bands. In addition, given the knowledge of an optimal directional beamforming vector, large antenna arrays have been shown to overcome both the severe signal attenuation in mmWave as well as the interference problem. However, fundamental limits on achievable learning rate of an optimal beamforming vector remain. This paper considers the problem of adaptive and sequential optimization of the beamforming vectors during the initial access phase of communication. With a single-path channel model, the problem is reduced to actively learning the Angle-of-Arrival (AoA) of the signal sent from the user to the Base Station (BS). Drawing on the recent results in the design of a hierarchical beamforming codebook [1], sequential measurement dependent noisy search strategies [2], and active learning from an imperfect labeler [3], an adaptive and sequential alignment algorithm is proposed. An upper bound on the expected search time of the proposed algorithm is derived via Extrinsic Jensen-Shannon Divergence. which demonstrates that the search time of the proposed algorithm asymptotically matches the performance of the noiseless bisection search up to a constant factor. Furthermore, the upper bound shows that the acquired AoA error probability decays exponentially fast with the search time with an exponent that is a decreasing function of the acquisition rate. Numerically, the proposed algorithm is compared with prior work where a significant improvement of the system communication rate is observed. Most notably, in the relevant regime of low (-10dB to 5dB) raw SNR, this establishes the first practically viable solution for initial access and, hence, the first demonstration of stand-alone mmWave communication

Explore and Eliminate: Optimized Two-Stage Search for Millimeter-Wave Beam Alignment

Swift and accurate alignment of transmitter (Tx) and receiver (Rx) beams is a fundamental design challenge to enable reliable outdoor millimeter-wave communications. In this paper, we propose a new Optimized Two-Stage Search (OTSS) algorithm for Tx-Rx beam alignment via spatial scanning. In contrast to one-shot exhaustive search, OTSS judiciously divides the training energy budget into two stages. In the first stage, OTSS explores and trains all candidate beam pairs and then eliminates a set of less favorable pairs learned from the received signal profile. In the second stage, OTSS takes an extra measurement for each of the survived pairs and combines with the previous measurement to determine the best one. For OTSS, we derive an upper bound on its misalignment probability, under a single-path channel model with training codebooks having an ideal beam pattern. We also characterize the decay rate function of the upper bound with respect to the training budget and further derive the optimal design parameters of OTSS that maximize the decay rate. OTSS is proved to asymptotically outperform state-of-the-art beam alignment algorithms, and is numerically shown to achieve better performance with limited training budget and practically synthesized beams.

Codebook Design for Beam Alignment in Millimeter Wave Communication Systems

Owing to abundant spectrum resources, millimeter wave (mmwave) communication promises to provide Gbps data rates, which, however, may be restricted by large path-loss. Thus, antenna arrays are commonly used along with beam alignment (BA) as an important step to achieve the array gain. Efficient BA relies on the beam training codebook design. In this paper, we propose a new hierarchical codebook to achieve uniform BA performance with low overhead. To better elaborate on the design principle, a single-path channel model is considered first to frame the proposal. The codebook design is formulated as an optimization problem, where the ripple in the main/side lobes is constrained such that each training beam is close to the ideal one with a flat magnitude response and a narrow transition band. Then, we propose an efficient algorithm to find such a beam training codebook. Furthermore, we derive closed-form expressions of the BA misalignment probability or error rate of the proposed beam training codebook. Our results reveal that using the proposed codebook, the error rate of tree-search-based BA exponentially decreases with the SNR for a given channel, and linearly decreases in the log–log coordinate axis for a fading channel. We further propose a power allocation scheme used in different training stages to further improve the BA performance. Finally, the proposed framework is extended to the more complex case of multi-path channels. Numerical results confirm the effectiveness of the proposed training codebook and power allocation scheme as well as the accuracy of the performance analysis.

Millimeter Wave Beam Alignment: Large Deviations Analysis and Design Insights

In millimeter wave cellular communication, fast and reliable beam alignment via beam training is crucial to harvest sufficient beamforming gain for the subsequent data transmission. In this paper, we establish fundamental limits in beam-alignment performance under both the exhaustive search and the hierarchical search that adopts multi-resolution beamforming codebooks, accounting for time-domain training overhead. Specifically, we derive lower and upper bounds on the probability of misalignment for an arbitrary level in the hierarchical search, based on a single-path channel model. Using the method of large deviations, we characterize the decay rate functions of both bounds and show that the bounds coincide as the training sequence length goes large. We go on to characterize the asymptotic misalignment probability of both the hierarchical and exhaustive search, and show that the latter asymptotically outperforms the former, subject to the same training overhead and codebook resolution. We show via numerical results that this relative performance behavior holds in the non-asymptotic regime. Moreover, the exhaustive search is shown to achieve significantly higher worst-case spectrum efficiency than the hierarchical search, when the pre-beamforming signal-to-noise ratio (SNR) is relatively low. This study hence implies that the exhaustive search is more effective for users situated further from base stations, as they tend to have low SNR.

PERFORMANCE RELIABILITY OF DS-CDMA MOBILE COMMUNICATION SYSTEM

Applications of DS-CDMA in mobile communication systems, in forward link and reverse link, imply certain precautions against near–far effect (NFE), multi-access (co-channel) interference (MAI/CCI), and multipath fading. In this paper, two multi-user detection schemes are proposed to enhance the reliability of DS-CDMA system against NFE and MAI for both reverse link and forward link applications. The first scheme, reverse link multistage CCI cancellation (RLCCI) scheme, is derived for a single path channel model and is based on minimization of estimation error between the received signal and its projections on spreading sequences subspace. The second scheme, forward link CCI (FLCCI) cancellation scheme is based on keeping a simple yet robust decoder at the mobile station (MS), reducing the negative impact of CCI, and enhancing CCI positive contributions. FLCCI minimizes the negative impact of CCI by adjusting the magnitudes of vulnerable spreading codes to compensate in advance for CCI losses. Block diagrams, mathematical models, performance analysis and reliability of both cancellation schemes against NFE, MAI, and external noise are discussed in details. The improvements in BER and overall performance are evaluated using Monte Carlo simulation for both schemes.