Iterative MIMO Detection with Modified FP Algorithm

rithm

In this Section, we present the iterative MIMO detection with modified FP algo- rithm. Fig. 5.2 illustrates the algorithm flow. The modules highlighted are modified for the new algorithm. The algorithm can be summarized in the following six steps, and the detailed description of each step is presented afterwards.

• Step 1: Initialization

• Step 2: Compute bounds

– Compute the accumulated a priori information metric – Compute the branch metric

– Compute the path metric

– Compute lower and upper bounds

• Step 3: Enumerate the tree node

• Step 4: Go to next or upper level if out of bounds

• Step 5: Update the Node

• Step 6: Found candidate signal vector

– Save the vector

– Update bounds

– Go to upper level

The algorithm starts from Step 1 Initialization, which initializes all the parame- ters required for the tree node search. These parameters include the received signal and upper triangular matrix from preprocessing, the search sphere radius, branch metric, path metric, and the accumulated a priori information metric, etc. Then the search starts from the top level of the tree and computes the lower and upper bounds for the tree node enumeration in Step 2. We include the computation of the accumulated a priori information metric in addition to the branch metric and path metric. And the a priori information is also utilized in the computation of the boundaries.

In Step 3, the tree node is enumerated in an ascending order starting from the lower bound. Step 4 directs the search one level up or one level down depending

Step1:Initialization

Step 2: Compute bounds

Within the Upper bound?

Step 4a: Go to next level Input Parameter Already Lowest level Enough candidates? Step 4b: Go to Upper level Step 6: Update Candidate Yes Yes No Yes No No The a priori informaion Compute extrinsic LLRs Update accumulated a priori information metric Update accumulated path metric Step 3: Enumerate Node Compute accumulated a priori information metric Compute accumulated branch metric Compute accumulated path metric Compute lower bound Compute upper bound Step 5: Updating metrics Save candidate in the candidate list Update radius with

accumulated path metric Update bounds Terminate Already Top level? No Yes

Figure 5.2: Algorithm flow chart for iterative MIMO detection with modified FP algorithm

on whether the enumerated node is within the boundaries. Step 5 updates the accumulated a priori information metric, the branch metric, and the path metric if the tree node survives. Once the search reaches the lowest level with surviving tree node, it means a candidate signal vector is found. Step 6 saves the candidate signal vector and continue to search other possible candidates.

Mathematically, given Y0_{, R, the a priori information P(X}b_{), and the radius}

C0, the modified FP algorithm can be outlined as follows:

1. Set tree search level index i := 2NT −1, path metric ϑi := 0, branch metric

ζi := 0, accumulated a priori information metric δi := 0, constellation index λj := 0, j ∈[0,2NT −1], constellation set Φ, and current radiusd:=C

0

. 2. If (d < ϑi)

Go to Step 4. Else {

Compute the lower bound Li := l

Y_i0−ζi−√d−ϑi

Ri,i

m

5.4 Iterative MIMO Detection with Modified FP and SE Sphere Decoder 119

Compute the upper boundVi := j

Yi0−ζi+√d−ϑi

Ri,i

k

,

λi :=idx(Li,Φ)−1,idx(·) is the operator that finds the index in constel-

lation set Φ.}

3. λi :=λi+ 1, Xbi := Φ(λi)

If (Xbi ≤ Vi) b

Xi Within the interval, go to Step 5.

Else

b

Xi Outside the interval, go to Step 4.

4. If (i== 2NT −1)

Go to Step 7. Else

Go back to upper level i:=i+ 1, then go to Step 3. 5. If (i >0) {

Update branch metric ζi−1 := 2NPT−1

k=i

Ri−1,kXbk,

Update accumulate a priori information metric δi :=δi−1+ 2σw2 lnP(Xbi)

Update path metric ϑi−1 :=ϑi+|Y

0

i −ζi−Ri,iXbi|2−δi,

Go to next leveli:=i−1, then go to Step 2. } Else if(i== 0)

Go to Step 6. 6. If (d > ϑi+|Y

0

i −ζi−Ri,iXbi|2−δi){

Updating the radius d:=ϑi+|Y

0

i −ζi−Ri,iXbi|2−δi,

SaveXb in candidate list U,

Go back to upper level i:=i+ 1, then go to Step 7.} 7. If (C0 is within Upper bound)

If(List has less points as required)

Increase the radius C0, then go to Step 1. Else

Terminate.

The new algorithm differs from the original FP algorithm in that it includes a priori information metric δi accumulated along the way of tree search. The path metricϑi is determined not only by the accumulated branch metricζi, but also the

additional accumulated priori information metric δi. If the visited nodes diverge

path metricϑiand a dramatically reduced search radius in (i+1)thlevel. Therefore,

invalid paths will be identified and pruned at an early stage, and the number of tree nodes visited will be reduced.