Intelligent reflecting surface (IRS) has been regarded as an emerging technology, which can significantly enhance the coverage and capacity of next-generation wireless networks. An accurate and easy-to-use channel model is essential to the deployment and evaluation of IRS-assisted communication systems. In this paper, we propose a 3D geometry-based channel model for the IRS-assisted multiple-input-multiple-output (MIMO) communications, and its corresponding parameters are obtained by channel measurement to better capture the underlying propagation characteristics. First, a cascaded channel model considering the relationship between the reflection amplitude and the angle of signal is presented. With the cascaded channel model, a channel coefficient generation procedure based on the 3GPP technical report 38.901 is proposed for IRS-assisted communication systems. To generate the cascaded channel, a response function that satisfies the reciprocity of uplink and downlink channels is derived. Then a channel measurement campaign at 3.7GHz is carried out to obtain some small-scale parameters for the IRS scenario. Finally, the proposed statistical channel model is implemented on a system-level simulation platform and some channel characteristics are analyzed to validate its rationality.

Extremely large-scale multiple-input multiple-output (XL-MIMO) system providing more degrees of freedom and beamforming gain, can effectively increase the capacity and coverage of wireless networks, which has become one of the key technologies for 6G. However, the near-field and non-stationary effects will appear as the array aperture expands. Therefore, existing channel models such as COST 2100 are extended to model these propagation effects. Considering the actual deployment of extremely large-scale antennas, this paper further extends the COST 2100 channel, including a) extending BS VR to 3D modeling to support the non-stationary characteristics of large-scale arrays in vertical and horizontal dimensions; b) extending the distribution of MS VR in vertical height to support user equipments (UEs) which are distributed on floors at different heights; c) extending models to support spatially consistent propagation characteristics between multi-TRPs. Finally, we show that our modeling method is reasonable through parameter tuning and simulation, and it can be used to evaluate the system performance of large-scale MIMO with different deployment morphologies.

Extremely large antenna array (ELAA) is one of the most promising technologies in 5G-Advanced (5.5G), which is equipped with hundreds or even thousands of antennas at base station (BS), to meet the requirements of higher rate and spectral efficiency. To verify the characteristics of ELAA channel, including spatial non-stationary, near-field spherical wavefront effect and channel hardening, a measurement campaign is performed, which is equipped with 128-element antenna array at BS on 5.3 GHz with 160 MHz bandwidth in a typical urban macro (UMa) scenario. Based on this, the correlation of power angular spectrums (PAS) between sliding windows of antenna array and the standard deviation (STD) of angular spreads (AS) are defined as the metrics to measure the level of variations of ELAA channel along with the antenna array. The correlation goes slightly down while the distance of two subarrays of the BS is larger than 0.6 m and the STD of AS changes in the range from 1° to 8°. The STD of normalized channel gain is also given to measure the channel hardening. Due to the power imbalance along with the antenna array, it decreases non-linearly with the increasing number of antennas. Meanwhile, the comparisons between measurement and simulations by 3GPP TR 3S. 901 and modified COST 2100 are given to show the necessity of the modifications on the current channel model. All of above analyses show that the modified COST 2100 channel model has a better match with the ELAA measurement.

Nowadays, the demand for data traffic increases dramatically, which has posed significant challenge on the current infrastructures of cellular networks. To tackle the challenge, the massive multiple-input-multiple-output (MIMO) technology has been proposed, which can improve spectral efficiency greatly, and attract a lot of attentions in industry and academic. In spite of the great potential benefits of massive MIMO, the property of massive MIMO channel with hundreds or thousands of antennas is still an open problem. In this paper, we try to look into deeply the spatial correlation of the channels for extremely large aperture array (ELAA) with some measurements. Specifically, we analyze the correlation between two users’ channels. We also propose a novel metric to characterize the performance of multiuser MIMO (MU-MIMO), which will be used to analyze the MU-MIMO channel later. At last, we study the sinlge-user MIMO (SU-MIMO) channel in terms of the distribution of singular values and also establish the connection between the spread of singular values and UE correlation under special case.

In this paper, properties of the channel multipath are analyzed for the industrial environment, where there are full of metallic boxes, operating platforms, tubes and also the robotic arms which are used to operate manufacturing process instead of human. The analysis is implemented based on ray tracing simulation. For base station configuration, we use the multiple transmission and reception points (multi-TRP), as it is a proper choice for future 5G and advanced systems. Multi-TRPs is beneficial to meet the requirement of ultra-reliable low latency communication (uRLLC), which is crucial for wireless communication between robotic arms and base station. Under such circumstance, it is found the delay spread in such factory is quite large. Some conclusion are derived from the simulations, including the effect of user mobility together with robotic arms.

Reconfigurable intelligent surfaces (RISs) are 2-D metasurfaces, which can intelligently manipulate electromagnetic waves by low-cost near passive reflecting elements. RIS is viewed as a potential key technology for the sixth-generation (6G) wireless communication systems mainly due to its advantages in tuning wireless signals, thus smartly controlling propagation environments. In this article, we aim at addressing channel characterization and modeling issues of RIS-assisted wireless communication systems. First, the concept, principle, and potential applications of RIS are given. An overview of RIS-based channel measurements and experiments is presented by classifying frequency bands, scenarios, system configurations, RIS constructions, experiment purposes, and channel observations. Then, RIS-based channel characteristics are studied, including reflection and transmission, the Doppler effect and multipath fading mitigation, channel reciprocity, channel hardening, rank improvement, far field, near field, and so on. RIS-based channel modeling works are investigated, including large-scale path loss models and small-scale multipath fading models. Finally, future research directions related to RIS-assisted channels are also discussed.

In a realistic fifth generation (5G) massive multiple-input multiple-output (MIMO) system, hardware constraints often pose challenges towards network design that are not sufficiently considered in the literature. In this work, we consider a time division duplex (TDD) network where user equipments (UEs) are equipped with N> 1 antennas for receiving in the downlink (DL) but only with a single antenna for transmitting in the uplink (UL). Thus it is not possible to learn the complete downlink channel in a single timeslot from the uplink utilizing channel reciprocity. In this paper, we propose a novel solution based on deep learning with auxiliary input of the estimated single antenna channel in the uplink to accomplish the downlink channel completion for full rank transmission from the base station (BS). We use synthetic data for deep learning training and testing provided by the stochastic quasi-deterministic radio channel generator (QuaDRiGa). Evaluation results show that our work outperforms existing deep learning based algorithms and can provide highly effective recovered channels even with complex channel data and low compression ratio.

One challenge for FDD massive MIMO communication system is how to obtain the downlink channel state information (CSI) at the base station. Except for traditional codebook feedback through uplink pilot transmission, some channel reciprocity properties can be utilized through uplink channel estimation and channel parameter estimation algorithms. In this paper, the uplink and downlink channel reciprocity properties are analyzed. It is theoretically proved that not all multipath parameters for FDD downlink and uplink channels are equivalent. Therefore, the so called full reciprocity property does not hold while the partial reciprocity property holds. Moreover, the channel measurement campaign is conducted to verify our theoretical analysis. Finally, in order to support the partial reciprocity property, the revision for the standardization 5G channel model is proposed as well. With the contribution of this paper, the FDD massive MIMO system transmission scheme design could be led to the right direction.

Artificial intelligence (AI) based downlink channel state information (CSI) prediction for frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems has attracted growing attention recently. However, existing works focus on the downlink CSI prediction for the users under a given environment and is hard to adapt to users in new environment especially when labeled data is limited. To address this issue, we formulate the downlink channel prediction as a deep transfer learning (DTL) problem, and propose the direct-transfer algorithm based on the fully-connected neural network architecture, where the network is trained in the manner of classical deep learning and is then fine-tuned for new environments. To further improve the transfer efficiency, we propose the meta-learning algorithm that trains the network by alternating inner-task and across-task updates and then adapts to a new environment with a small number of labeled data. Simulation results show that the direct-transfer algorithm achieves better performance than the deep learning algorithm, which implies that the transfer learning benefits the downlink channel prediction in new environments. Moreover, the meta-learning algorithm significantly outperforms the direct-transfer algorithm, which validates its effectiveness and superiority.

In this paper, by using a dual-band channel sounder equipped with omnidirectional antennas, we have measured and investigated the propagation parameters including path loss and shadowing at 1.79 and 4.9 GHz in the typical non-line-of-sight (NLOS) urban macrocell (UMa) scenario. Two different large-scale channel models, the alpha-beta-gamma (ABG) model and the close-in model with a frequency-weighted path loss exponent (CIF), are derived according to the channel measurement data. Finally, we compare the parameter values, shadow fading (SF) standard deviations, and prediction errors of the two models, and evaluate the accuracy and sensitivity with respect to the measurement data. The numerical results show the improvement in the channel fading estimation of the CIF model compared with the ABG model.

Massive multiple-input multiple-output (MIMO) transmission is one of the key technologies utilized in the fifth generation (5G) wireless communication system. For the algorithm design and the performance evaluation of massive-MIMO, channel characterization based on real measurements is necessary. In this paper, we introduced a measurement campaign conducted in a Line-of-Sight (LoS) scenario of a suburban outdoor environment. The channel sounder is equipped with a 64-element transmitter array and a 64-element receiver array. Multiple aspects of massive-MIMO channel characteristics are considered, including the power delay profile, the K-factor and the delay-spread. We found that for the outdoor LoS scenario considered, the polarization plays an important role generating orthogonal channels observed through large-scale antenna arrays.

Connecting unmanned aerial vehicles (UAVs) by using cellular networks can significantly expand the civil applications of UAVs, due to much a larger connectivity range and low cost. However, the low-altitude air-to-ground (ATG) channels are different from the traditional terrestrial mobile access channels, and hence need to be characterized specifically. In this paper, a measurement campaign and modeling of the aerial access channels between a UAV and base station (BS) in the typical urban macro-cell (UMa) and rural macro-cell (RMa) scenarios are presented. The channels were sounded at 2.412 GHz and 919 MHz with the horizontal ranges of 420 meters and 10 kilometers, respectively, in the two scenarios. The transmitter equipped with two omnidirectional antennas was fixed on a fourrotor UAV which flew horizontally at various altitudes from 25 to 150 meters. The receiver was installed on the top of five-storey buildings to emulate a BS. The path loss (PL) was measured and the statistical models have been proposed which are based on the corresponding 3GPP territorial channel models but adjusted by adding correction factors (CFs). The CF is relevant to the UAV height in the UMa scenario. For the RMa scenario there is a breaking point with respect to the horizontal distance and hence a segmented function for the CF is proposed. The new PL models can help to establish the ATG channel models and support the design of air-borne access technologies for the LTE networks.

Both the conventional time-division-multiplexing channel sounder and the horn-antenna-rotating millimeter-wave channel sounder suffer from a serious problem that significant time consumptions are inevitable when sounding a spatial channel in 3- dimensions. In this paper, a novel channel sounder utilizing Hybrid BeamForming (HBF) techniques is presented which can complete a 3D channel measurement in microseconds, facilitating wideband MIMO channel sounding in time-variant cases, such as vehicular scenarios. The sounder is equipped with 64 transmitter (Tx) antennas and 64 receiver (Rx) antennas. The Tx makes use of digital beamforming (DBF) to compose 8 directive radiation patterns by superimposing multiple weighted patterns each generated with 8 antennas through analog beamforming. The Rx receives signals through 8 parallel front-end chains each connected to an 8- element antenna array. A 26-GHz channel measurement campaign was conducted by using the sounder in a line-of-sight indoor environment. The results demonstrate the applicability of the sounder in measuring millimeter-wave channels. Moreover, special notes are given on the appropriate usage of parameter estimation algorithms to processing the HBF channel sounding data.

Matrix completion aims to find the missing entries from incomplete observations using the low-rank property. Conventional convex optimization based techniques for matrix completion minimize the nuclear norm subject to a constraint on the Frobenius norm of the residual. However, they are not robust to outliers and have a high computational complexity. Different from the existing schemes based on solving a minimization problem, we formulate matrix completion as a feasibility problem. An alternating projection algorithm (APA) is devised to find a feasible point in the intersection of the low-rank constraint set and fidelity constraint set. To achieve resistance to outliers, the fidelity constraint set is modeled as an ℓp-ball, where the ball center corresponds to the observed data. Furthermore, there is no stepsize within the framework of APA. Convergence of the APA is analyzed and the local linear convergence rate is established. Simulation results demonstrate the efficiency, accuracy, and outlier robustness of the APA.

In this paper, by using a multiple-input multiple-output (MIMO) antenna array, a channel measurement campaign in outdoor environments is introduced. The measurement campaign captures the spatial characteristics of centimeter wave (cm-wave) propagation at the center frequency of 26 GHz . By using the parametric approach of the Space-Alternating Generalized Expectation-maximization (SAGE) algorithm, the channel characteristics in the delay and spatial domains are extracted, and compared with the channel model below 6 GHz. Our analysis shows that the channel dispersions in the delay and directional domains are smaller at the 26 GHz. Furthermore, single-user (SU)-MIMO and multi-user (MU)-MIMO channel matrix properties are investigated, and show that the MU-MIMO channel has good orthogonal property. It implies that MU-MIMO will be one promising MIMO technique in cm-wave band.

In this contribution, two measurement campaigns are reported which were conducted in urban areas of Shanghai for characterizing the radio channels in an operating Universal Mobile Telecommunications System (UMTS). The signals on the common pilot channels transmitted by multiple NodeBs (NBs) are used to calculate the channel impulse responses (CIRs). A Space-Alternating Generalized Expectation-maximization (SAGE) algorithm is applied to extracting the delays, Doppler frequencies and complex attenuations of multiple specular path components from the CIRs. Based on the delay spreads calculated, the channels are categorized into three types, i.e. the single-path, two-path and multi-path. Based on the measurements at more than 1400 locations for 74 NBs, the statistics of system-level channel characteristics, such as the percentage of channels per NB belonging to different categories and the length of the distance within which the same channel category is observed are extracted.

In this contribution, the 3-dimensional (3D) channel characteristics, particularly in the elevation domains, is extracted from measurement data collected in typical urban macro- and micro-environments in the city of Xi'an, China. Stochastic channel models are established based on high-resolution multi-path parameter estimates. Additionally, a modified spatial channel model (SCM) for the line-of-sight (LoS) scenario is proposed where the LoS polarization matrix is defined more reasonably than in the conventional models. Measurement results demonstrate the consistency of the revised model with the reality.

In this contribution, both theoretical studies and measurement results are reported for investigating the anisotropic property of propagation channels with respect to (w.r.t.) the (linear) polarizations of the transmitter (Tx) and receiver (Rx) antennas. Under the assumption that the channel impulse response (CIR) is polarization isotropic, analytical expressions are derived for the K-factor and delay spread as functions of Tx-Rx polarizations, and furthermore, our deduction also shows that the rank of the signal subspace spanned by a multi-polarized narrowband channel is upper-bounded. Based on the measurements conducted in indoor scenarios, empirical CIRs measured with 12 Tx- and 2 Rx-polarization directions are applied to investigating the channel polarization anisotropy. It can be observed that the measured channels exhibit properties inconsistent with the theoretical results deduced under the polarization-isotropy assumption, implying that the realistic indoor propagation channels can be anisotropic w.r.t. the Tx-Rx polarizations.

The new multichannel/multicarrier technologies have drawn great attention recently to support high data rate in mobile multiple-access environments, such as the carrier aggregation (CA) as a part of 4G LTE-Advanced enhancement. On the way to the development of multicarrier technologies, there is a considerable need to understand and utilize the correlation properties of distinct subchannels, which, however, has not been reported in the literature. Based on the extensive indoor ultra-wideband (UWB) channel measurement, this paper develops a new approach to analyze the correlation of the large and small-scale fading of arbitrarily separated subchannels. The approach avoids the high complexity and cost of the conventionally probing the multiple subchannels simultaneously using channel sounders which would be too complicated to implement. We first propose a modified CLEAN algorithm to reliably extract channel impulse responses (CIRs) from the measured pulse response waveforms with substantially varying noise floor. Then the cross-correlation of the fading of two distinct subchannels, the autocorrelation of the fading of a single subchannel and the correlation of the multipath profile over a small area are analyzed. The study has revealed how significantly the channel response would change when the receiver travels from room to room or just over a distance of dozen of wavelength, and how two separated subchannels are correlated. In our view, the acquired new insights on subchannel correlations could provide guidelines for efficient designs and performance predictions of multicarrier communication systems.

In this paper, a channel modeling method based on random-propagation-graph is elaborated, validated, and applied to characterizing time-variant channels observed in typical environments for high-speed railway wireless communications. The advantage of the proposed method is that the frequency-tempo-spatial channel coefficients, as well as the multi-dimensional channel impulse responses in delay, Doppler frequency, direction of arrival (i.e. azimuth and elevation of arrival) and direction of departure are calculated analytically for specific environments. The validation of the proposed method is performed by comparing the statistics of two large-scale parameters obtained with those described in the well-established standards. Finally, stochastic geometry-based models in the same format as the well-known spatial channel model enhanced (SCME) are generated by using the proposed method for the high-speed scenarios in the rural, urban, and suburban environments.

In this paper, propagation channel measurement data obtained by using the wide-band multiple-input-multiple-output (MIMO) channel sounder - PROPsound - is applied to analyzing the cross-correlation behavior of spatial-polarimetric (SP) channels in indoor environments. Four antennas are selected from the transmitter (Tx) array and from the receiver (Rx) array to form a 2×2 spatial MIMO channel, with each spatial element consisting of co-located ±45°-polarized antennas. The characteristics of the resultant 16 × 16 narrow-band SP Channel Correlation Matrix (CCM) are studied for five indoor environments of different types. Results show that the Kronecker model proposed in the 3rd Generation Partnership Project (3GPP) TS36.101, which describes the SP CCM as the Kronecker product of the separate Tx and Rx spatial CCMs, and the 4×4 polarimetric CCM, is inapplicable in indoor scenarios. As an alternative, we propose to consider the cross-correlation coefficient of SP channels as a random variable, and apply its empirical statistics for stochastic modeling. Results also show that the empirical distribution of the off-diagonal elements of SP CCM is distinctive with respect to the types of environments.

In this paper, we consider asynchronous two-way wireless relay networks with amplify-and-forward protocol (AF- TWRN), where the distributed space-time code (DSTC) is utilized without synchronization among relays to assist the communication between two terminals. We analyze the pairwise error probability (PEP) behavior of DSTC for AF-TWRN under frequency-selective channels. From our analysis, it is seen that of the paths from one terminal to relays and from relays to another terminal, those with smaller diversity order result in an overall system performance bottleneck. Considering both the timing errors among relays and the multipath fading, we then propose a family of distributed convolutional space-time codes (DCSTC) for AF-TWRN such that the full diversity order can be achieved. Finally, various numerical examples are provided to corroborate the analytical studies.

In cooperative communication networks, the performance of the distributed space-time code (DSTC) will be severely degraded if the timing synchronization among relay nodes are not perfect. In this paper, we propose a systematic construction of the so called distributed linear convolutional space-time code (DLCSTC) for multipath fading channels that does not require the synchronization assumption. We derive sufficient conditions on the code design such that the full cooperative and multipath diversities can be achieved under the minimum memory length constraint. Then we design DLCSTCs that both have the trace-orthonormality property and achieve the full diversity. We also study the diversity property of the DLCSTC with suboptimal receivers. We show that the proposed codes can also achieve the full diversity for asynchronous cooperative communications with ZF, MMSE and MMSE-DFE receivers under frequency-selective channels. Finally, various numerical examples are provided to corroborate the analytical studies.

In most cooperative communication works, perfect synchronization among relay nodes is assumed in order to achieve the cooperative diversity. However, this assumption is not realistic due to the distributed nature of each relay node. In this paper, we propose a family of distributed space-time trellis code (DSTTC) that does not require the synchronization assumption. It is shown that the proposed DSTTC has minimum memory order, and the construction of such DSTTCs is equivalent to using the generator matrices that have full row rank, regardless of sub-matrices shifting problem. Here, a sub-matrix corresponds to the generator matrix of a relay node under frequency-selective channels. We derive sufficient conditions on the code design such that the full cooperative and multipath diversities can be achieved. By further studying the diversity product, we design the DSTTCs which can achieve full diversity and the maximum coding gain through the exhaustive computer search. The newly proposed codes exhibit good properties, e.g., high energy efficiency and low synchronization cost, and can be applied to distributed wireless networks. Finally, various numerical examples are provided to corroborate the analytical studies.

In cooperative communication networks, the performance of distributed space-time code will be severely degraded if the timing synchronization among relay nodes is not perfect. In this letter, we propose a systematic construction of the so called distributed linear convolutional space-time code (DLCSTC) for multipath fading channels that does not require the synchronization assumption. We derive sufficient conditions on the code design such that the full cooperative and multipath diversities can be achieved under the minimum memory length constraint. Then we design DLCSTCs that both have the traceorthonormality property and achieve the full diversity. We show that the proposed codes can also achieve the full diversity for asynchronous cooperative communications with ZF, MMSE and MMSE-DFE receivers under frequency-selective channels. Finally, various numerical examples are provided to corroborate the analytical studies.

Exploiting the desirable properties of cyclic group coding, we develop a full-rate differential distributed space- frequency coding (DSFC) in the frequency domain for broadband non-regenerative wireless relaying systems. The pairwise error probability analysis demonstrates that our scheme guarantees a diversity order of Gdles min{ML1, ML2}, where M is the number of the relay nodes, and L1and L2 are the number of taps of source-to-relay and relay-to-destination channels, respectively. A novel subcarrier allocation method without channel state information (CSI) at any node is proposed to improve the diversity product. Moreover, for an arbitrary number of relays, a competitive non-regenerative DSFC proposed by Zhang et. aL, is extended to differential transmission incorporated with the proposed subcarrier allocation method for fair comparison. Both theoretical analysis and simulation results confirm that the proposed DSFC outperforms Zhang's scheme significantly in the differential case.

This paper analyzes the performance of limited feedback (LFB) beamforming in multiple-input multiple-output (MIMO) distributed antenna systems (DAS). The averaged effective signal-to-noise ratio (ESNR) is derived for both the case where all antenna ports are used for transmission (blanket transmission, BT) and the case where only one of the ports are selected (port selection, PS). Based on the derived ESNR, we propose two adaptive LFB beamforming schemes for MIMO DAS, which switch between BT and different PS schemes. Through simulations, we confirm the analytical studies and investigate the performance of different LFB beamforming schemes.

In this paper, we study the asynchronous cooperative diversity schemes employing the amplify-and-forward (AF) protocols over the frequency-selective channel. We consider three time-division-multiple-access (TDMA) based cooperation protocols and derive the corresponding pairwise error probabilities (PEP). From our analysis, it is seen that of the paths from the source to relays and from relays to the destination, those with smaller diversity order result in the bottleneck for the overall system performance. We propose a new type of the distributed space-time trellis code (DSTTC) that can achieve full diversity for the asynchronous transmission by utilizing a specifically designed generator matrix. The optimal DSTTCs with the minimum memory order are found by the exhaustive computer search. Finally, various numerical examples are provided to corroborate the analytical studies.

In most cooperative communications works, perfect synchronization among relay nodes is assumed in order to achieve cooperative diversity. However, this assumption is not realistic due to the distributed nature of each relay node. In this paper, we propose a family of distributed space-time trellis code (DSTTC) that does not require the synchronization assumption. It is shown that the proposed DSTTC can achieve full cooperative and full multipath diversities for the asynchronous transmission by utilizing a specifically designed generator matrix. We derive sufficient conditions on the DSTTC with the minimum memory order. Finally, various numerical examples are provided to verify the analytical studies. The newly proposed codes exhibit good properties, e.g. high energy efficiency and low synchronization cost, and can be applied to distributed wireless networks.

In most cooperative communications works, perfect synchronization among relay nodes is assumed in order to achieve cooperative diversity. However, this assumption is not realistic due to the distributed nature of each relay node. In this paper, we propose a new distributed space-time coded transmission (DSTCT) scheme for asynchronous cooperative communications under frequency-selective channels. First, a novel transmission protocol, in which each relay is labelled in delay-ascending order, is proposed. Second, the pairwise error probability and the design criterion of DSTCT are derived. Finally, based on the proposed transmission protocol and the design criterion, a new DSTCT scheme for asynchronous cooperative communications is proposed. Theoretical analysis and simulation results show that this scheme can achieve both full cooperative diversity and full multipath diversity.

In this paper, we study the performance of the multiple-input multiple-output macrodiversity transmission with limited feedback. The downlink scenario, where multiple transmitters serve the user simultaneously, is considered. We find it necessary to modify the model of the quantized channel by Jinal (2006) such that the phase ambiguity in the vector quantization procedure can be characterized. Using the modified model, we show that the conventional limited feedback methods cannot obtain the macrodiversity gain even when the size of the codebook is asymptotically large, and that the macrodiversity gain can be attained by adding only one bit of phase feedback. Our analysis can apply to both random vector quantization and any fixed codebook setup, and is verified by the simulation results.

In most cooperative communications works, perfect synchronization among relay nodes is assumed. However, this assumption is not realistic due to the distributed nature of each relay node. In this paper, we consider the downlink in a MIMO cellular network utilizing two-hop transmission protocols with fixed infrastructure relay stations (RS) to enhance coverage and data rates. We propose a family of distributed space-time trellis code (DSTTC) for two RSs without the synchronization assumption. It is shown that the construction of the proposed DSTTCs is equivalent to using the generator matrices that have full row rank regardless of sub-matrices shifting problem, where a sub-matrix corresponds to the generator matrix of a RS under frequency-selective channels. Finally, various numerical examples are provided to verify the analytical studies.