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We now quickly describe space-time trellis codes (STTCs) and layered space-time codes (LSTs) because many recent HARQ schemes are designed for them.

STTCs are another important subfamily of STCs. They were first introduced in [37]. They are an extension of the traditional trellis codes, introduced in Chapter 2, to MIMO systems [54]. The performance improvement is due to both increased diver- sity and Euclidean distance compared with the uncoded systems. Unfortunately, the decoding complexity of STTCs increases exponentially with the diversity and trans- mission rate [55].

A STTC encoder is now briefly introduced. Assuming a constellation with M points is used, the encoder generates nt symbols for every mb = log2(M ) information

bits for each time slot. These nt symbols are transmitted from nt transmit antennas simultaneously. Each of these nt symbols, Xi i = 1, · · · , nt, at time T is given by [3]

Xi= mb X p=1 vp X l=0 g_l,ip bp_{T −l} mod M, i = 1, 2, · · · , nt (3.46)

where bp_{T −l}is the pth _{bit in a group of m}

b bits at time T − l and is stored in the lthshift register of the path for the pth _{bit stream, and g}p

shift register and the memory order of the path for the pth_{bit stream, respectively. This} encoder is illustrated in Fig 3.2 [3]. Because memory units are used in the encoder, a trellis diagram can be drawn according to the memory states associated with the inputs. Hence, STTCs can be decoded using the Viterbi decoding algorithm.

Figure 3.2 A STTC encoder [3].

Another type of MIMO system, which is quite different from all previously in- troduced MIMO systems, is the layered space-time (LST) architecture. This type of MIMO system requires the number of receive antennas nrto be equal to or greater than the number of transmit antennas nt. It can provide very high rate, but requires pow- erful signal processing technique such as successive interference cancellation employed by the receiver [3].

Here, the vertical layered space-time (VLST) scheme, is briefly introduced. It is used in the HARQ scheme of [56] which will be briefly considered in Section 4.1.1. In the

VLST scheme, the information bit stream is demultiplexed into nt substreams. These

The decoding complexity can be significantly reduced by using successive interfer-

ence cancellation instead of using joint detection. The decoding procedure is normally

carried out by using interference suppression combined with interference cancellation. The interference suppression can be done by using QR decomposition interference sup- pression or interference minimum mean square error suppression. After the interference suppression is done, the nt transmitted symbols are ordered in terms of their received SNR and the transmitted symbol with the highest received SNR is decoupled from the

other nt− 1 symbols. This symbol is estimated and a hard decision is made. Then,

the interference caused by this symbol is subtracted out and the transmitted symbol with the second highest receive SNR is decoupled and estimated. A hard decision is made based on the estimation. This process is repeated many times until the decod- ing procedure is finished. Because each symbol is decoded individually, the decoding complexity is linear with the number of transmit antennas [6]. However, this decoding procedure indicates that, if an error is made for one symbol, all the decisions for the following symbols are likely to be erroneous.

3.6 SUMMARY

In this chapter, MIMO wireless communication systems were introduced. They use multiple transmit antennas and multiple receive antennas to achieve larger channel capacity than SISO systems. They normally use specially designed STCs to achieve good performance. A good STC can be obtained if it is designed according to special design criteria for STCs [3] [6]. Two design criteria were discussed. The first one is called the trace criterion, which is used for MIMO systems with diversity gain ≥ 4 and the second one is called the rank and determinant criteria, which is used for diversity gain < 4.

STBCs including OSTBCs, QOSTBCs and NOSTBCs were described in detail in this chapter. OSTBCs have simple decoding algorithms and can achieve full diversity gains. But they cannot provide coding gains and full rate OSTBCs for MIMO systems with more than two transmit antennas do not exist. QOSTBCs can achieve higher rates than OSTBCs, but their decoding algorithms are more complicated. NOSTBCs can achieve even higher rates, but normally their decoding algorithms are even more complicated.

The good performance offered by MIMO systems has lead to their recent use with HARQ schemes. These existing HARQ schemes for MIMO systems will be introduced in Section 4.1. Three novel HARQ schemes will be proposed in Section 4.2. They use the NOSTBCs of [12] due to the good performance and high rate these NOSTBCs can offer.

The design of hybrid automatic-repeat-request (HARQ) schemes for multiple input multiple output (MIMO) systems has recently attracted lots of research attention due to the good performance MIMO systems can achieve. HARQ schemes for MIMO com- munication systems can be designed by combining techniques introduced in previous chapters. Several recently proposed HARQ schemes for MIMO systems are summa- rized in this chapter. Some of them are motivated by the ARQ schemes for single input single output (SISO) systems introduced in Chapter 2 [13] [30] [36] [57]. In addition, some novel HARQ schemes for MIMO system are proposed in this chapter. We also discuss adaptive modulation and coding (AMC) in this chapter. It can be used to achieve better performance by reconfiguring the transmitter according to the current CSI. The current channel state information (CSI) is estimated by the receiver and fed back through a feedback channel.

This chapter is organized as follows. In section 4.1, a general summary of some recently proposed HARQ schemes and AMC schemes is presented. In Section 4.2, the novel HARQ schemes proposed in this thesis are described. In the last section, we introduce how to apply adaptive modulation based on the water filling principle to the proposed HARQ schemes.