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In this paper, we propose the receiver structure for Multiple Input Multiple Output (MIMO) Interleaved Single Carrier-Frequency Division Multiple Access (SC-FDMA) where the Frequency Domain Equalization (FDE) is firstly done for obtaining the tentative decision results and secondly using them the Inter-Symbol Interference (ISI) is cancelled by ISI canceller and then the Maximum Likelihood Detection (MLD) is used for separating the spatially multiplexed signals. Furthermore the output from MLD is fed back to ISI canceller repeatedly. In order to reduce the complexity, we replace the MLD by QR Decomposition with M-Algorithm (QRD-M) or Sphere Decoding (SD). Moreover, we add the soft output function to SD using Repeated Tree Search (RTS) algorithm to generate soft replica for ISI cancellation. We also refer to the Single Tree Search (STS) algorithm to further reduce the complexity of RTS. By examining the BER characteristics and the complexity reduction through computer simulations, we have verified the effectiveness of proposed receiver structure.

Recently MIMO transmission techniques with multiple transmit and receive antennas are widely used to achieve the spatially multiplexed transmission and to increase the transmission rate in wireless communications. For MIMO spatially multiplexed transmission, MLD is known as the optimum signal separation method at the receiver side, which attains the minimum BER. However, when the number of transmit antenna and the modulation levels are increased, MLD needs very high computational complexity and the reduction of complexity becomes a problem [

In

where

We call

Next,

quency domain ISI replica is made through multiplying

replica

ponents due to the transmit signals other than time

where

ration of spatially multiplexed transmission is done using MLD. The total number of candidates of receive replica for MLD is

where the matrix size is

and the candidate receive replica for MLD is obtained as

the ISI cancelled receive signal and the candidate MLD replica in frequency domain is calculated as

where

output of

The number of candidate replicas in MLD increases exponentially as

where

where

As

As the tree search method for

search along the path is no more needed, thus the amount of calculation is saved. Therefore, when the initial sphere radius is small, the complexity reduction becomes more effective. In other words, the higher the

By using QRD-M instead of MLD in the receiver structure in

Then the channel matrix

The Hermitian transpose

hand side.

The squared metric for minimization using

Using

By using SD instead of MLD in the receiver structure in

We aimed to obtain the soft output from the SD in

point

the 1st bit being 1.

ing 0 and 1 respectively. In SD, there exist some paths for which searches are not made in the tree. In order to calculate the bit LLR, the path for bit “0” and the path for bit “1”, both of which have minimum path metrics, have to be evaluated. For this evaluation, we have used the RTS [

In RTS, using (13) and the

In STS, the path metrics for calculating the bit LLR’s are evaluated using the single search of the tree. The basic idea of STS follows that every path metric and its search depth are stored in the list and monitored. When the evolution of all the path metrics in the list does not occur during the tree search, the search of specific branch is saved and this results in complexity reduction. At the initial stage, the values in the list are all set to infinity. In

In STS algorithm, the list in

example, its value is compared with all

find that the further search of this branch does not lead to the evolution of the path metric. Accordingly we stop

the search and move to the calculation of

the list and the bit LLR’s are calculated using (14) and (15).

Computer simulations are made for the system in

Number of UE | 4 |
---|---|

Number of transmit antennas in each UE | 4 |

Number of receive antennas at BS | 4 |

Modulation formats | QPSK |

Number of total subcarriers | M = 256 |

Number of subcarriers assigned to each user | N = 64 |

Symbol length of QPSK | T |

Cyclic prefix length | 4T/ |

Channel model between each transmit and receive antenna | Equal power 16 paths quasi-static Rayleigh fading channel |

Interval of delay time | T/4 |

Subcarrier assignment | IFDMA |

Channel estimation | Perfect at BS |

FDE | Nulling (MMSE) |

Initial radius setting for SD (SE algorithm) | QRD-M (m = 1) |

Number of iterative feedbacks in the receiver | 0,1,3 |

the lower bound of BER where the ISI cancellation is perfect, which means the demodulated bits for ISI cancellation are error-free. In

From

From

hard ISI cancellation. We find that at average

this means the perfect ISI cancellation is possible at this receive SNR value.

From

From

time is about 15 times higher than QRD-M. However, above

proaches to QRD-M. This is because for high average

small value. Although the RTS can produce the soft output, the RTS needs a lot of path metric calculation leading relatively high computation time. The STS which is the improved version of RTS shows the computation

time almost the same as the SD in low

compared with the RTS. However, the computation time of STS is almost constant over entire

In this paper, we have proposed the low BER receiver structure for the interleaved SC-FDMA on the uplink MIMO frequency selective fading channels. In the proposed receiver, using the tentative decision results obtained from the MMSE nulling (FDE), the ISI components are cancelled and the MLD is then used for separating the spatially multiplexed signal streams. The reliable output from MLD is again fed back to the ISI canceller to reduce the residual ISI. Furthermore we improve the complexity of MLD by replacing it with QRD-M or SD. We have verified the BER characteristics of the proposed receiver with MLD, QRD-M or SD through computer simulations. The receiver with SD achieves the same BER as the one with MLD, i.e., ML solution, whereas the QRD-M has the inferior BER because of its quasi-ML solution. We have also verified that the complexity of SD is very much improved compared with MLD especially in high

This study has been supported by the Scientific Research Grant-in-aid of Japan No. 24560454 and Sharp cooperation.