1

CDMA Receiver using Compact Neural Network and Hardware Annealing Debdutta Bhattacharya Roll No. 05EC1008 Department of Electronics and Electrical Communication Engineering Indian Institute of technology, Kharagpur – 721302, India E-mail: [email protected]

Abstract A neural network based CDMA (Code Division Multiple Access) receiver for multi-user detection is proposed. The Compact Neural Network based receiver is used for Optimal Multi-User Detection instead of comparators as in a conventional CDMA receiver. This is done to avoid near-far problems wherein a signal from a near user has more energy and may get wrongly accepted when the user is unwanted as compared to a far user whose signal will have comparatively lesser power. Implementation of the Compact Neural Network is done by Hardware Annealing which is used to avoid local minima and find optimal solution and the global minimum and thus improve performance. This receiver shows improved performance as compared to conventional CDMA receivers. Problem Definition CDMA or Code Division Multiple Access is a wireless communication method in which each user is assigned a code and has a CDMA receiver is attuned to receive signals sent by that code by that user. Users having different codes share a single RF channel. Now, in the conventional receiver, the detector/receiver is prone to make wrong decisions if a signal is received from an unwanted near user and the desired user who is far from the receiver. This is commonly known as the near-far problem. A Compact Neural Network based receiver with Hardware Annealing Optimization is proposed here for removal of that problem. This is the main approach to the problem. A compact CDMA receiver has a Core that replaces the comparators and has a feedback network of neurons all interconnected thus helping remove the near far effect. (Fig. 3) Moreover even after having a core, the system may wrongly detect local minima in the energy function that is used to characterize the core and provide that as a solution. To remove this and ensure that the global minimum is detected, Hardware Annealing is also added to the design. Details about the problem The model consists of a matched filter each for the symbol of each user. It is followed by a Compact Neural Network Core that helps in the decision making stage. It is implemented by Hardware Annealing so that solutions found in the decision stage are not affected by local minimas obtained from the energy function obtained. The aspects of the model that are discussed are: • A comparison between the conventional and Neural Network based detector • Neural Network Core • Hardware Annealing

1

2 The layout of the proposed receiver is as shown (Fig. 1):

Figure 1 – The layout of the proposed CDMA receiver

The Conventional Detector vs. Optimal Multi-User Detector with Compact Neural Network 1. The Conventional Detector The CDMA receiver has K matched filters for K users and thus responds to and filters out K different signature waveforms. R (t) that is received signal is made by the K users using their signature waveforms sk (t) K

r (t ) = ∑ bk (i ).sk (t − iT ) + n(t ) k =1

Where

[

, t ∈ iT , (i + 1)T

]

(1)

sk (t) has a string of bits.

It thus recognizes every active user’s symbol at a specified interval. A matched filter for that purpose does the following function (Refer to Fig.2): ( i +1)T

y

(i ) k

=

∫

r (t ).sk (t − iT ).dt

(2)

iT

and the output that is, the presence/absence of the Kth user’s symbol, is determined by the sign of

yk (i ) given by bk ( i ) bk ( i ) = sgn( yk (i ) )

(3)

2

3 The outputs bk can be represented as a matrix bout as shown: (Eq. 4) bout = [ b1(i) b2(i) … bk(i) ]

(4)

Figure 2 – The layout of the conventional CDMA receiver

2. The Optimal Multi-User Detector The multi user detector has a Compact Neural Network core after the matched filter stage (as shown earlier in Fig 1). Neural Network Core The inter-neuron weights are given by T

hij = ∫ si (t ).s j (t ).dt gives H ∈ R K ×K

(5)

0

The equation that gives the output (this network has feedback): y = Hb+n (6) The cost function has to be minimized thus maximizing the logarithm of the maximum likelihood function. T

K

0

k =1

bOMD = arg min b∈{−1,1}K ∫ [r (t ) − ∑ bk sk (t )]2 dt

(7)

which can be written as

3

4

bOMD = arg min b∈{−1,1}K 0.5bT Hb − bT y

(8)

Now, the energy function of a Compact Neural Network is given by:

E = −0.5vTy Mv y − vTy d

(9)

This can be compared to the output of the OMD and thus the OMD can be made using a Compact Neural Network by having M = -H and d = y.

Figure 3 – Internal Structure of the Neural Network Core (K=5)

Hardware Annealing Hardware annealing is the method of using a cellular neural network with feedback which is actually an optimization problem in which the deepest minimum is the optimum solution to the problem. Once mapping is done, the system can evolve by neuronal dynamics (change of gain-weights) until steady state is reached. Here, convergence can be achieved very fast in a fraction of a microsecond using VLSI neural network processors. It does not require any iterative stochastic procedure and henceforth can be very fast. The landscape of the network energy function is first adapted so that the whole annealing process does not get stuck at a local minimum at the beginning of searching for optimal solutions by adjusting each neuron to a low voltage gain. Then, the hardware annealing searches for the globally minimum energy state by continuously increasing the gain of neurons. The globally optimal equilibrium state is reached when each neuron is at its maximum voltage gain.

4

5

Figure 4 – A Cellular Neural Network Considering a m*n CNN with neurons (as shown in Fig. 4) with piecewise linear transfer function f ( g ( x)) whose gain function given by:

v y = f ( gvx ) = {1 ; vx > 1/ g v y = f ( gvx ) = { gvx ; − 1/ g ≤ vx ≤ 1/ g

(10)

v y = f ( gvx ) = {−1 ; vx < −1/ g The hardware annealing is performed by continuously controlling the gain g (t) of the neuron, which is assumed to be the same for all neurons throughout the network. The continuous change in g (t) changes it from what it was and brings it closer to 1 at which point the network is stabilized. As shown in Eq. 11, this helps optimize the energy function. The graphical representation of the gain function is shown in Fig. 5 (linear activation function used)

Figure 5 – Piecewise Linear Characteristic of a CNN The energy function of the neural network may be derived as:

E = −0.5∑ i, j

∑

C ( k ,l )∈N r ( i , j )

A(i, j; k , l )v yij vvkl + 1/ 2 gRx ∑ (v yij ) i, j

5

2

6 = −∑

∑

i , j C ( k ,l )∈N r ( i , j )

B(i, j; k , l )v yij v ykl + ∑ I b v yij i, j

= −0.5 y M g y − y b T

T

(11)

Here is a block diagram of the variable gain cell with an analog multiplier.

Figure 6 – Block diagram of a variable gain cell Simulation and Results Comparison is made between the performance of a conventional detector and a CNN based CDMA receiver. A K=2 synchronous and noiseless case is considered. The original signal is a = [-1,-1]T at a given time. The two users have different signal powers to simulate the near-far problem. The normalized cross correlation of the two users’ signatures is h. The range of h =[-0.9,-0.8,-0.7,0.6…,0]. ‘r’ is the ratio of signal powers of the two users and the range of r=[100, 100.1,100.2,…101]. The output of matched filter Y is sent to the Neuron Core for detection as shown in Fig 1.

Log(r) vs. h Figure 7(a) – Conventional CDMA receiver

Log(r) vs. h Figure 7(b) - CDMA receiver using CNN with sigmoid function

Log(r) vs. h Figure 7(c) - CDMA receiver using CNN with sigmoid function and Hardware Annealing

6

7 The cross marks on the graphs are Failure Points. As can be seen, with increasing correlation values, the probability of failure increases. The conventional receiver has failure points for correlation values between -0.2 to -1 and for r ranging from 100 to 101. The CDMA receiver with CNN has failure points for correlation = -1 and r between 100.5 to 101. The CDMA receiver also with hardware annealing feature has failure only for r=10 and h=-1. Summary This paper proposes the use model of a CDMA receiver using Compact Neural Network. This CNN is easy to make onto VLSI chips along with Hardware Annealing. Also a comparison between the conventional receiver, a CNN based receiver and that coupled with Hardware Annealing is done, we see that the Hardware Annealing and CNN based receiver gives best performance (that is least failure). Such CDMA receivers also provide a robust solution to the near-far problem. It is also easy to implement due to its modular architecture structure. Future projections The CDMA receiver model that is discussed in this paper has used Compact Neural Network and Hardware Annealing to find optimal solutions to the energy function. Other neural architectures in the proposed model of CDMA receiver The near-far problem necessitates the use of a neural network feedback based structure. So, other iterative neural network based methods or Hopfield Neural Network (HNN) based algorithms may be used to implement the same receiver. The problem in HNN implementation may be convergence to a local minimum which may further be removed by iteration. The implementation can be done by HNN chips. Extend the use of the Compact Neural Network Core The CNN core that is used may be used in other applications as well in the decision stage where we have to compare between inputs as in this case. Such applications may include optical receivers, audio receivers as well. Thus, we can have more extensive use of the compact neural network core used here.

References [1] Bang, S.H., Sheu, B.J., Chou, E.Y., "A hardware annealing method for optimal solutions on cellular neural networks," Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on , vol.43, no.6, pp.409-421, Jun 1996 [2] Chen D.C., Bing J. Sheu, Theodore W. Berger, "A Compact Neural Network Based CDMA Receiver for Multimedia Wireless Communication," iccd, p. 99, 1996 IEEE International Conference on Computer Design (ICCD'96), 1996 [3] Kechriotis G.I., Manolakos E.S., "A hybrid digital computer-Hopfield neural network CDMA detector for real-time multi-user demodulation," Neural Networks for Signal Processing [1994] IV. Proceedings of the 1994 IEEE Workshop, vol., no., pp.545-554, 6-8 Sep 1994 [4] Kechriotis, G.; Manolakos, E.S., "A hybrid digital signal processing-neural network CDMA multi-user detection scheme," Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on [see also Circuits and Systems II: Express Briefs, IEEE Transactions on], vol.43, no.2, pp.96-104, Feb 1996

7