**ABSTRACT**

The concept of deploying a large number of antennas at the base station, often called massive multiple-input multiple-output (MIMO), has drawn considerable interest because of its potential ability to revolutionize current wireless communication systems. Most literature on massive MIMO systems assumes time division duplexing (TDD), although frequency division duplexing (FDD) dominates current cellular systems. Due to the large number of transmit antennas at the base station, currently standardized approaches would require a large percentage of the precious downlink and uplink resources in FDD massive MIMO be used for training signal transmissions and channel state information (CSI) feedback. First, we propose practical open-loop and closed-loop training frameworks to reduce the overhead of the downlink training phase.

We then discuss eﬃcient CSI quantization techniques using a trellis search. The proposed CSI quantization techniques can be implemented with a complexity that only grows linearly with the number of transmit antennas while the performance is close to the optimal case. We also analyze distributed reception using a large number of geographically separated nodes, a scenario that may become popular with the emergence of the Internet of Things. For distributed reception, we ﬁrst propose coded distributed diversity to minimize the symbol error probability at the fusion center when the transmitter is equipped with a single antenna. Then we develop eﬃcient receivers at the fusion center using minimal processing overhead at the receive nodes when the transmitter with multiple transmit antennas sends multiple symbols simultaneously using spatial multiplexing.

** DOWNLINK TRAINING TECHNIQUES FOR FDD MASSIVE MIMO SYSTEMS: OPEN-LOOP AND CLOSED-LOOP TRAINING WITH MEMORY**

The ceiling eﬀect can be eﬀectively reduced by exploiting the temporal channel correlation. Although temporal correlation is present essentially for all wireless communication systems, this correlation is not widely exploited in most MIMO channel estimation and training works. Training for massive MIMO systems should leverage temporal correlation of the channel to maximize the beneﬁt of having a large number of antennas.

The base station then uses the fed back signal as the training signal for the i-th fading block. The training signal selection at the user is based on using channel prediction to track the statistics of the channel at the i-th fading block conditioned on the user’s side information as explained in open-loop training with memory. The conceptual explanation of closed-loop training with memory is given in Fig. 2.2.

** NONCOHERENT TRELLIS CODED QUANTIZATION: A PRACTICAL LIMITED FEEDBACK TECHNIQUE FOR MASSIVE MIMO SYSTEMS**

From Fig. 3.3, we see that the TCQ system consists of a source constellation, a trellis-based decoder (for source quantization), and a convolutional encoder (for source reconstruction).

The construction of the feedback sequence is done using a trellis decoder. As is done in traditional decoding of convolutional codes, the encoding process is represented using a trellis showing the relationship between states of the encoder along with input and output transitions. The trellis with input/output state transitions corresponding to the convolutional code in Fig. 3.4 is shown in Fig. 3.6.

**TRELLIS-EXTENDED CODEBOOKS AND SUCCESSIVE PHASE ADJUSTMENT: A PATH FROM LTE-ADVANCED TO FDD MASSIVE MIMO SYSTEMS**

TEC can be implemented using any trellis quantizer. In this work, we adopt the Ungerboeck trellis and convolutional encoder because of their simplicity and good performance. As shown in Fig. 4.2, each state has four branches diﬀerentiated with inputs and even or odd outputs.

As we can see in Fig. 4.10, TE-SPA is also beneﬁcial for spatially correlated channels even with less feedback overhead than TE-LTE which quantizes h[k] directly. It is important to point out that TE-SPA for spatially correlated channels has additional feedback overhead.

**CODED DISTRIBUTED DIVERSITY: A NOVEL DISTRIBUTED RECEPTION TECHNIQUE FOR WIRELESS COMMUNICATION SYSTEMS
**

We consider a network consisting of a transmitter, a fusion center, and N geo-graphically separated receive nodes. The conceptual ﬁgure of our system model is shown in Fig. 5.1.

We plot the results of the scenarios 1 and 2 in Figs. 5.5a and 5.5b, respectively. In the ﬁrst scenario, the proposed scheme and the naive approach are comparable with each other. This is reasonable because the proposed coding structure is not intended to increase the achievable rate. However, the proposed scheme outperforms the naive approach in the second scenario. This is because the second node that processes the imaginary component of the transmitted symbol is in a deep fade in the naive approach, resulting in signiﬁcant achievable rate degradation.

**QUANTIZED DISTRIBUTED RECEPTION FOR MIMO WIRELESS SYSTEMS USING SPATIAL MULTIPLEXING**

With the knowledge of H and y at the fusion center, we can implement diﬀerent kinds of receivers considering complexity and performance. We ﬁrst develop an optimal ML receiver and low-complexity ZF-type receiver. Then, we discuss the performance of receivers regarding system parameters such as ρ and K. We also explain a possible modiﬁcation of the ZF-type receiver and analyze the achievable rate of quantized distributed reception.

In Fig. 6.7, we plot the average achievable rate deﬁned in (6.19) to evaluate the beneﬁt of spatial multiplexing in distributed reception. Due to the computational complexity, we only consider Nt = 2 with K=3 and 5 receive nodes.

** CONCLUSIONS**

In this dissertation, we proposed eﬃcient downlink training and CSI quantization techniques to design practical FDD massive MIMO systems. We also studied distributed reception scenarios and proposed superior quantization and decoding methods for the cases of single and multiple transmit antennas. In Chapter 2, we proposed open and closed-loop training frameworks using successive channel prediction/estimation at the user for FDD massive MIMO systems. By exploiting prior channel information such as the long-term channel statistics and previous received training signals at the user, channel estimation performance can be signiﬁcantly improved with only small length of training signals in each fading block compared to open-loop/single-shot training.

Moreover, with a small amount of feedback, which indicates the best training signal to be sent for the next fading block, from the user to the base station, the downlink training overhead can be further reduced even when the transmitter lacks any kind of side information, e.g., statistics of the channel. In Chapter 3, we proposed an eﬃcient channel quantization method, dubbed NTCQ, for massive MIMO systems employing limited feedback beamforming. While the quantization criterion (maximization of beamforming gain or minimization of chordal distance) is associated with the Grassmann manifold, the key to the proposed NTCQ approach is to leverage eﬃcient encoding (via the Viterbi algorithm) and codebook design (via TCQ) in Euclidean space.

Source: Purdue University

Author: Junil Choi