 Open Access
 Total Downloads : 299
 Authors : S. Sheshana Priya, K. Senthil Kumar
 Paper ID : IJERTV3IS20578
 Volume & Issue : Volume 03, Issue 02 (February 2014)
 Published (First Online): 24022014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
FPGA Implementation of High Throughput MIMO Detectors Based on Path Preserving Trellis Search Algorithm
S. Sheshana Priya1, K. Senthil kumar2
1PG Student, 2Assistant professor
Department of electronics and communication engineering DMI college of engineering, Chennai602013, India
Abstract In this paper , novel path preserving trellis search algorithm (PPTS) and its high speed VLSI architecture (FPGA) for softoutput multipleinputmultipleoutput (MIMO) detection. In MIMO receiver design as the computational complexity increases exponentially with the number of antennas. So in order to overcome this complexity PPTS algorithms are introduced. The PPTS algorithm is a hardwarefriendly dataparallel algorithm because the search operations are evenly distributed among multiple trellis node for parallel processing. The PPTS detector is guaranteed to have soft information for every possible symbol transmitted on every antenna so that loglikehood ratio (LLR) for each transmitted data bit can be more accurately formed. Simulating result shows that our proposed scheme PPTS algorithm can achieve low search complexity and high throughput mechanism.
Keywords FPGA, MIMO, soft output MIMO detectors , shortest path algorithms.
I.INTRODUCTION
Multipleinputmultipleoutput (MIMO) system have potential to increase spectral efficiency by transmitting independent data streams on multiple antennas. MIMO technologies have been adopted in many new wireless standards such as Wi MAX and WLAN. Softoutput MIMO detection poses significant challenges to the MIMO receiver design as the computational complexity increases exponentially with the number of antennas. However, the optimal softdecision detector, the maximum a posterior detector, will consume enormous computing power and require tremendous computational resources which make it infeasible to be used in a practical MIMO receiver. So efficient algorithms used to reduce the MIMO detection complexity. The MIMO detection problem is usually tackled based on treesearch algorithms. The treesearch algorithms can be often categorized into the depth first search algorithm and the breadthfirst search algorithm. The sphere detection algorithm is a depthfirst treesearch algorithm to find the closest lattice point. To provide soft information for outer channel decoders, a modified version of the sphere detection algorithm, or soft sphere detection algorithm, is introduced. There are many implementations of sphere detector sphere detector suffers from nondeterministic complexity and variabletime throughput. The sequential nature of the depth first treesearch process significantly limits the throughput
of the sphere detector especially when the SNR is low. The kBest algorithm is a fixedcomplexity algorithm based on the breadthfirst treesearch algorithm . But this algorithm tends to have a high sorting complexity to find and retain the best candidates, which limits the throughput of the detector especially when k is large. In treesearch algorithms is that the counter hypotheses for certain bits are missing due to tree pruning. As a consequence of missing counter hypotheses, the magnitude of the LLRs for certain bits cannot be determined, which will lead to performance degradation. To avoid the missing counterhypothesis problem and to reduce the search complexity, we investigate high performance MIMO detection algorithms and highspeed VLSI architectures.

SYSTEM MODEL
We consider a spatialmultiplexing MIMO system with Nt transmit antennas and Nr receive antennas (Nr > Nt) . The MIMO transmission can be modeled as
Y = Hs + n (1)
Where H is a Nr * Nt complex matrix and is assumed to be known perfectly at the receiver, S is a Nt * 1 transmit symbol vector S [S0 S1..SNt1 ]T , is a received vector Y= [Y0 Y1.YNr1]T, and is a vector of independent zeromean complex Gaussian noise entries with variance per real component. A real bitlevel vector XK = [ XK,0 XK,1 XK, MC 1 ]T is mapped to the complex symbol SK , where the bth bit of Xk is denoted as Xk,b and is the number of bits per constellation point. Throughout this paper, the complex symbol and its associated bit vector XK will be used interchangeably.
The optimal MAP detector is to compute the loglikelihood ratio (LLR) value for the a posteriori probability (APP) of each transmitted bit. Assuming there is no a priori information for the transmitted bit, the LLR APP of each bit Xk,b can be computed
s:x exp(1/22 y H. s 2)
, = ln k,b=+1
s:xk ,b =1 exp(1/22 y H. s 2)
(2)
With maxlog approximation,
Note that to form LLR for bit Xk,b , both the ML hypothesis and the counterhypothesis of bit Xk,b are required. Otherwise, the magnitude of the LLR will be undetermined. If a (sorted) QR decomposition of the channel matrix according to H=QR is used, where Q and R refer to an Nr * Nt unitary matrix and Nt * Nr an upper triangular matrix is changed to
every transmitted bit, finding one shortest path is not enough. We want to find multiple paths which cover every node in the trellis graph. The multiple shortest paths problem is defined as follows. For each k, q node in the trellis graph, find a shortest path from root to sink that must visit this node k, q . The corresponding shortest path weight is related to the symbol probability . If we can find such a conditional shortest path for each node in the trellis,
, = 1/22( min
: , =1
min
: , =+1
())
(3)
we will then have one soft information value for every possible symbol transmitted on every antenna. As a result, we will have sufficient soft information values to avoid the
Where the Euclidean distance d(s),
=0
d(s) = = . 2 = =1 ) 2

PATHPRESERVING TRELLISSEARCH ALGORITHM
(4)
missing counterhypothesis problem. Thus, the LLR for every data bit can be formed accurately based on these soft information values.
1V. VLSI ARCHITECTURE
In this section, we describe VLSI architectures for the proposed PPTS detector. We introduce a fullyparallel
Computing the bit LLR in (3) requires searching for a ML
hypothesis and a counterhypothesis of this bit over a large search space. To reduce the search complexity and avoid the missing counterhypothesis problem, we introduce a path preserving trellissearch (PPTS) algorithm for soft MIMO detection.

Unconstrained Trellis Model
The Euclidean distance in (4) can be computed recursively. To visualize the recursion, we create a graph model, which resembles an unconstrained trellis. As an example, Fig. 1 shows the trellis graph for the 4Ã— 4 4QAM system. In this graph, nodes are ordered into Nt vertical slices or stages, where stage k corresponds to symbol Sk transmitted by antenna . The trellis starts with a root node and ends with a dummy sink node. The stages are labeled in descending order. In each stage, there are Q = 2 different nodes, where each node maps to a constellation point that belongs to a known alphabet. Thus, each transmitted symbol vector is a path from root to sink.
Fig 3.1 Trellis graph for the 4Ã—4 4QAM system

Multiple Shortest Paths Problem
We transform the soft MIMO detection problem into a multiple shortest paths problem. In the trellis graph, each trellis node , maps to a complex symbol sk such that each path from root to sink maps to a symbol vector S. A path weight is a measurement of the soft probability for nodes (symbols) on this path. To make a sof decision for
systolic architecture to achieve the maximum throughput performance, and a folded architecture to reduce area for lower throughput applications. For the sake of clarity, we describe a PPTS detector architecture with for the 4 Ã— 4 16 QAM system. It should be noted that the architecture described can be easily scaled for other values of and other MIMO configurations.

FullyParallel Systolic Architecture
The fullyparallel systolic architecture for Nt = 4 antenna system. This architecture is fully pipelined so that it can process one MIMO symbol in every clock cycle. In this architecture, the main processing elements include three path reduction units (PRUs), three path extension units (PEUs), four path selection units (PSUs), and four LLR calculation (LLRC) units. The detailed structures of these processing elements will be described in the following subsections.
2
1
The three PRUs and one PSU are employed to implement the path reduction algorithm. The main diagonal of the systolic array is related to the path reduction data flow. The PRU implements one main iteration loop of Algorithm by employing path reduction processors to simultaneously process Q nodes in a certain stage implements PSU0 the final selection step of Algorithm by using Q search units. The data flow for the path reduction is as follows. First, receives R, Y , and the precomputed , and it computes all the path candidates (i,j) in parallel, which are fed to the next PRU, i.e.,PRU2. Then,PRU2 computes (i,j) , which are fed to PRU1 , and so forth. Finally,PSU0 receives
0
(, ) from PRU1 and computes, which are fed to to
1
compute . The three PEUs and three PSUs are employed to implement the path extension algorithm. Each row (but the last) of the systolic array is related to the path extension data flow . The PEU implements one main iteration loop of Algorithm by employing path extension processors to simultaneously extend nodes in a certain stage. The PSU is used to implement the final selection step of Algorithm. The data flow for the path extension is as follows. To detect antenna, k 1, k1 number of the PEUs and 1 PSU are used. Let = k1 . First, PEUk,t receives (, ) from PRUK and
it computes Q(m)(k,i,t1,j), which are fed to PEUk,t1 . Next, PEU k,t1 computes Q(m) (k,i,t2,j) , which are fed to PEUk,t2 , and so forth. Finally, PSUk receives Q(m)(k,i,0,j) from PEU k,1 and computes (0)(k,i,0) , which are fed to LLRCk.
fig 4.1 structure of PRU

PRU
The structure of the PRU is shown in Fig 4.1 The PRU is used to implement the path reduction algorithm . The PRU employs Q = 16 path reduction processors to process all the nodes in a certain stage in parallel. Each path reduction processor contains one minimum (min) finder unit (MFU) and one path calculation unit (PCU), where the MFU is used
1
to select the best paths (, )from the incoming path candidates () (, ) the PCU is used to compute the new extended path candidates ()(i,j).

MFU: The MFU is used to select the best M = 2 paths
From QM = 32 path candidates. Fig. 10 shows the block diagram for the MFU unit which finds the minimum value Z0 and the second minimum value Z1 from its 32 data inputs (I0 toI31). The MFU is comprised of 16 CMP (comparison) units, 15 variable size CS (compare and select) units, and one MIN unit. The CMP unit compares two data inputs and
, and outputs the smaller one (or the winner): , and the larger one (or the loser):L= max(A,B) , and the sign:S=(AB).
Outputs W of the CS unit are candidates for the second smallest data among all the P inputs. he MFU takes data inputs and feeds them to 16 CMP units, where each CMP unit generates the winner and the loser of its two data inputs. The connection of the computational blocks in the MFU resembles a treelike structure. Every two CMP units are connected to one 4:3 CS unit, where the outputs of the 4:3CS unit are the winner of its four data inputs, and two candidates for the second winner. Every two 4:3 CS units are connected to one 6:4 CS unit, where the outputs of the 6:4 CS unit are the smallest data among its 6 data inputs ,and three candidates for the second smallest data .Similarly, every two 6:4 CS units are connected to one 8:5 CS unit, and two 8:5 CS units are connected to a final 10:6 CS unit. Finally, output of the 10:6 CS unit is the smallest data among the 32 data . Outputs of the 10:6 CS unit are the five candidates for the second smallest data among the 32 data inputs. A MIN unit is used to generate the second smallest data .

PEU:The PEU implements the path extension algorithm . The PEU has a very similar architecture to the PRU. . Each path extension processor contains one MFU and one PCU, where the MFU is used to select the best M paths (m) (k,i,t) from QM path candidates (m)(k,i,t,j) and the PCU is used to calculate the QM new extended path candidates (m)(k,I,t1,j.)
Fig 4.3, folded architecture for the PPTS detector

Throughput Performance of the Systolic Architecture
The proposed systolic MIMO detector architecture can provide very high throughput performance. This
architecture is fully pipelined so that it can process one MIMO symbol in every clock cycle. Generally, if we let the clock frequency be MHz, then the throughput (Mbps) for a Nt Ã—Nr QQAM system can be expressed as
= . 2.
(5)
As an example, assuming a system clock of 400 MHz, the systolic architecture can provide a throughput of 6.4 Gbps for a 4 Ã—4 16QAM system.

SIMULATION RESULT
fig 4.2 block diagram for the MFU which use 16 comparator units
The proposed systolic PPTS detector with can achieve a 6.4 Gbps throughput when running at 400 MHz. As can be seen from the table, the proposed detectors achieve very high data throughput while still maintaining a low area requirement. Compared to the KBest detector from the PPTS detectors M=2 with have a better area efficiency based on the area metric . The PPTS detector with achieves a balanced tradeoff between hardware complexity and error
performance ( 0.3 dB loss). The PPTS detector with achieves a closetooptimal error performance with a reasonable hardware cost. Therefore, the proposed detector is a viable solution for the Gbps MIMO detection problem as it achieves both high throughput performance and good error performance.
fig 5.1 Error performance of a coded 4Ã—4 4QAM MIMO using PPTS detection algorithm.
VLSI Implementation Result,
fig 5.2 simulation result for the proposed PPTS detector

CONCLUSION
We propose a novel softoutput MIMO detector architecture based on the PPTS algorithm. The PPTS algorithm is a search efficient algorithm based on a pathpreserving trellis search approach. We introduce a path reduction and a path extension algorithm to reduce the search complexity while still maintaining sufficient soft information values to form the LLRs. We avoid the missing counterhypothesis problem by keeping multiple paths during the trellis search process. Simulation results show that the PPTS algorithm can achieve very good error performance with a small M value. The proposed MIMO detector has great potential for application in the next generation Gbps wireless systems by achieving very high throughput and good error performance.

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