1. Advanced Wireless Receivers: Algorithmic and Architectural Optimizations
Suman Das
Rice University
Department of Electrical and Computer Engineering
&
Center for Multimedia Communication

2. Introduction Wireless is one of the fastest growing industries
100
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1993
1994
1995
1996
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1998
1999
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2001
millions of cell-phone users
Year
Source: Ericsson
“By 2002, a lot more cellular phones are going to have internet access than PCs.”
Larry Ellison , CEO, Oracle.
Wireless industry is in the midst of a phenomenal growth curve. Currently there are over 400 mil. Wireless users in the whole world and this number is expected to be quadrupled in the next four years. Larry Ellison, the chair of Oracle has predicted that by the year 2002, there will be more cellular phone with internet access than PC-s.

3. Ubiquitous wireless connectivity
Ad-hoc Network
Wireless Cellular
Bluetooth/
Home Networks
Wireless LAN
But popularity of the cell-phones is only part of the wireless story. In the future we are going to be covered by multiple overlapping layers of wireless connection. At office we will connect to the high-speed wireless LAN, at home our refrigerator will talk to our coffee-machine using Blue-tooth technology while at remote locations wireless technology will allow devices to form ad-hoc networks with others. Connectivity will be “anywhere anytime”.
But in order to achieve this dream we will have to overcome several challenges. In today’s presentation I will talk about some of these challenges, especially in the context of cellular systems and our solution.

4. Why advanced receiver algorithms?
The number of wireless subscribers growing
Multimedia data replacing voice traffic
Higher and varied data rate (144Kbps - 2Mbps)
Stricter quality of service (QOS)
Wireless bandwidth remains a critical resource
Current generation receivers are suboptimal
As already noted, the volume of cell-phone subscribers is growing at an amazing rate. Not only that, media rich-data is slowly replacing the traditional voice traffic. For this multimedia data the next generation cellular system have to support data rates ranging from 144 Kbps in the highways up to 2Mbps in the office environment. The quality of service also need to improve many fold. Unfortunately the wireless bandwidth is not growing at the same pace and it is found that the current generation wireless solution will be inadequate for such high volume of data.
Researchers have been looking for alternate receiver algorithms for this new system.The good news is it has been shown with more complex algorithms we can achieve higher performance.

5. Performance of advanced receivers6 8 10 12 14 16 4 -4 -2
bit error rate
SNR (dB)
Current receiver
Advanced receiver
Theoretical limit
This viewgraph is to show how much improvement in performance we can expect from these advanced algorithms. On the X-axis we have plotted the Signal to Noise ratio, which is a rough measure of the transmitter’s signal power and on the Y-axis we have plotted the bit-error rate. Lower the bit-error rate better is the performance. The black dotted curve at the top represents the performance of currently deployed algorithms, the red-curve at the bottom is the theoretical limit of the system (when there is only one user) and the intermediate green curve is the performance of one of the representative advanced receiver algorithms. It is evident that several order of performance improvement can be obtained through the use of these new algorithms.
So the question is why aren’t we using them?
Huge performance improvement

6. Computational requirements of advanced receivers
15 user system transmitting at 0.5Mbps needs
~20 Billion additions per second
~15 Billion multiplications per second
Requires 32 bit floating point precision
Need fifty 200 MHz floating point DSP-s!
The caveat is that,these proposed algorithms are also several orders of magnitude more complex. For example, in order to support 15 users transmitting data at the rate of 0.5Mbps these algorithms will require 20billion additions and 15 billion multiplications. Moreover all these operations need to be performed with 32 bit floating point arithmetic units. In short, we will require 50 floating point DSP-s running at 200MHz to sustain such a data rate.

7. My research Receiver design High performance Low complexity Approach
Algorithmic simplification
Efficient architectural mapping
This presents a dilemma. On one hand we will need to deploy some form of advanced receiver algorithms to support multimedia traffic but on the other hand the solution needs to be feasible for physical implementation in terms of power and hardware requirements.
Our approach will be to re-examine these class of advanced algorithms and propose new computationally efficient algorithms and their corresponding hardware implementations

8. Wireless channel model
Channel Effects
Background noise
Fading
Multiple paths
Multiple Users
Multiple Access Interference(MAI)
Noise
Reflected Paths
Base Station
Direct Path
Before we propose our solution lets take a closer look at the wireless channel.
The characteristic of the wireless channel is quite different than that of a wired channel. The transmitted signal is affected by background noise. Moreover the wireless channel has a fading characteristic. By that we mean the attenuation the transmitted signal experiences change over time and frequency. Moreover none of the wireless transmitters are in-directional. Hence multiple copies of the same signal will arrive after reflections. This is called the multi-path effect.
To further complicate the matter, there will be multiple users sharing the same channel. Hence a user’s signal will be affected by the presence of other user. And this is known as MAI.
User 1
User 2

9. Code Division Multiple Access (CDMA)
S(t)
Wideband CDMA
- technology of choice
Users distinguished by
spreading sequence
chip
Spreading
gain = 7
time
bit
Since multiple users share the same common channel, there needs to be a multiplexing scheme to distinguish between them. For next generation wireless system, CDMA has been chosen as the multiple access scheme. In this method the users are distinguished by a unique signature waveform. Each user modulates the transmitted bit by this spreading sequence. In this particular example in order to transmit the data bit 1, one would transmit the spreading waveform given by [ ]. The smallest unit of transmitted data is called a chip. The number of chips transmitted per bit is called the spreading gain of the system.
Received signal
K: # of users
P: # of paths
w: attenuation
t: delay
b: data bits

10. detected bits of all K users
CDMA system
TRANSMITTER
ENCODING
SPREADING
MODULATION
OTHER USERS
data
DECODING
DETECTION
DEMODULATION
CHANNEL ESTIMATION
RECEIVER
detected bits of all K users
A CDMA transceiver has two components. At the transmitter end, the data bits are first encoded by error-control coding and then spreaded using the spreading code. It is then modulated using carrier frequency for transmission.
The receiver consists of 3 modules, channel estimation or synchronization which estimates the delays and amplitudes of each path of each user. The detection module uses these information to detect the transmitted bits. The decoder is used to recover from any error incurred during the estimation process.
The advanced receivers employ multiuser algorithms. By that I mean, the data bits of all the users will be estimated simultaneously. However the effort in the research community so far has been to isolate the design of three modules. I will show that this approach is not only suboptimal in terms of performance, but also in terms of computational requirement.
Proposed advanced/multiuser receiver modules
Designed in isolation
Suboptimal design

11. Integrated receiver design
DECODING
DETECTION
DEMODULATION
CHANNEL ESTIMATION
RECEIVER
detected bits of all K users
Joint channel estimation and detection
Joint detection and decoding
My proposed solution can be broadly categorized as integrated receiver design approach. I will present my results in two steps. At first I will present solutions for a joint channel-estimation and detection and then I will extend the results to incorporate decoding.

12. Why separate channel estimation and detection?
Received signal
Chip-matched filter
Channel Estimation
Code-matched filter
Detection
delay
time
bi+1
The natural question obviously is why have people tried to compartmentalize the design. The reason is that the multiuser algorithms used for channel estimation and detection use two different statistics. For both the processes the received signal needs to be discretized. But while the detector works on the output of code-matched filter (which is output) at the bit level, the channel estimator takes in as input the output of chip-level matched filter. The processing window for the channel estimation starts at any arbitrary point. The delay of the path is essentially the distance between the start of the bit from this processing window.
However in order to compute the code-matched filter output, one has to start the filtering process from the bit boundaries. Since before channel estimation we don’t know the delays we cannot expect the arbitrary processing window for channel estimation will line up with the bit boundary. And the code matched filter has to start processing at the bit boundary of each user. Since each user has independent delay corresponding to each path, it will be incorrect to assume that the channel estimation processing window will match with all bit boundaries. Hence even though the chip matched filtering and code-matched filtering has some common operations, as also the computations done at the back-end channel estimation and detection algorithm one cannot take advantage of that since the two front ends need to process different data. bi ri
Processing Window for Chan. Est.
Operate on different statistics

13. Towards an integrated solution
Reuse computation from channel estimation step
Use same discretized filter output
Avoid alignment to bit interval of each user
Reduce computation
Save hardware
Our aim is to come up with a framework that will increase the efficiency of the two modules by more efficient data sharing as well as computation sharing.

14. Components of the observation vector
bit i = +1
bit i+1 = -1
wk,p
-wk,p
delay
wk,p
attenuation +

15. Matrix representation
bit i = +1
bit i+1 = +1 Uk Zk
bk(i) + other users
r = U Z bpreamble

16. Efficient statistics Parametric approach
Build channel model (number of paths)
Estimate delay, attenuation
Produce the code matched filter output
Our approach
Estimate effective spreading code (UZ)
Code matched filter y = (UZ)T r

17. Simulation parameters
System parameters
15 users
3 paths
Spreading gain - 31
Hardware platform
TI C62 and C67 EVM boards
64 KB each internal program & data memory
256 KB SBSRAM, 8 MB SDRAM (external)
Code-composer 1.0 to profile code

18. Effectiveness of integrated design10
Single User 10 -1
Multiuser algorithms
Parametric approach
UZ approach
Actual Parameters
bit error rate 10 -2 -3 10 10 -4 -4 -2 2 4 6 8 10 12 14 16
SNR (dB)
2dB gain in performance

19. Computational savings
Avoid extraction of actual channel parameters
Avoid realignment of data for code-matched filtering
Reduce intermediate storage requirement
Avoid divisions (28 cycles) and square-root (38 cycles) in DSP.

20. Fixed point behavior Fixed point advantages Speed Power Cost
Fixed point analysis
12 bit of precision required instead of 32 bits!
Pack two16 bit operations in 32 bit registers
More packing with
Saturation arithmetic
User power control!

21. Time requirement 2.39 X speedup 68.5 41.8 100 90 80 70 Normalized time60
41.8
2.39 X speedup 50 40 30 20 10
Unified
Synch + Detect
Original
16 bit fixed-point

22. Integrated receiver design
DECODING
DETECTION
DEMODULATION
CHANNEL ESTIMATION
RECEIVER
detected bits of all K users
Joint channel estimation and detection
Effective spreading code approach
Optimized detector design
Joint detection and decoding

23. Linear multiuser detector
Received signal r = (UZ) b + n
Channel estimation (UZ)
Matched filter output y = (UZ)T r
Linear detector R b + n= y solve
R = ((UZ)TUZ)
Size of the linear system (NK)
Direct inverse takes O((NK)3) operation
N block-length
K # of Users

24. Outline of the Kronecker algorithm
Correlation matrix is block-Toeplitz
Approximate it as a block-circulant system

25. Outline of the Kronecker algorithm
Kronecker representation
Isolates structure and the matrix blocks
Fourier transform converts it to a block-diagonal system
Computationally optimal
Solve N independent order K system iteratively

26. Speedup in detector 90 80 83.1 Kbps Complexity O(N2K3) Vs
O(NK2 + KNlogN) 70 60 50
Achievable data rate (Kbps) 40 30 20
10.4 Kbps 10
Decorrelator
Kronecker

27. Pipelining and parallelization
Mostly matrix based operations
Detector - iterative algorithm
Pipeline various iterations
Parallelize operations
Add more functional units
Distribute data across functional units
Distribute computations

28. Projected computation time
600
30 adders and multipliers
564.5 Kbps.
DSP + Coprocessor support
500
400
Achievable data rate (Kbps)
300
DSP
only
200
154.3 Kbps
100
20.75 Kbps
Base
Multiuser
Algorithm
Hardware Pipelining
Pipelining + Parallelization

29. Integrated receiver design
DECODING
DETECTION
DEMODULATION
CHANNEL ESTIMATION
RECEIVER
detected bits of all K users
Joint channel estimation and detection
Effective spreading code approach
Optimized detector design
Joint detection and decoding

30. Maximum a-posteriori (MAP) decoding
TRANSMITTER
ENCODING
SPREADING
MODULATION
OTHER USERS b d
Received signal: r = UZd + n
Optimum decoding rule
Constrained optimization problem
Decode all users simultaneously
Exponential complexity in number of users

31. Single-user detection and decoding
Suboptimum alternatives
Isolate detection and decoding y1 yK b1 ^ bK r
MF K
MF 1
Decoder 1
Decoder K . .

32. Decoding matched filter outputs10
MF+Viterbi
Optimal 10 -1 -2
BER 10 10 -3 -4 10 1 2 3 4 5 6 7 8
SNR(dB)
Huge performance loss!

33. Iterative detection and decoding
^ yc
= (UZ)Tc(r- (UZ)IdI)
User of concern c, interfering users I
r = (UZ)cdc + (UZ)IdI + z
Estimate dI
Eliminate interference:
Estimate dc for the next step
Complexity linear in number of users

34. Reduction in decoding complexity
Convolutional code
Coded bits depend on past data bits
Performance improves with memory length
Viterbi algorithm for decoding
Complexity exponential in memory length
Our suboptimal approach
Maximal weight basis decoding
Complexity quadratic in memory length

35. Joint detection and decoding performance10
MF + Viterbi -1 10
Iter1 + Subopt
Iter1 + Viterbi -2
Iter3 + Subopt 10
BER
Optimal -3 10
Rate = 1/2
k = 7 -4 10 -5 10 1 2 3 4 5 6 7 8
SNR (dB)

36. Joint detection and decoding
Huge performance gain.
Suboptimal approximation -
Insignificant performance loss
Significant computational gain
Architecture for suboptimal decoding?
Viterbi algorithm - butterfly architecture
Have a sliding window implementation

37. Summary of contributions
Integrated channel estimation and detection model [wcnc]
Optimized detection algorithm [PIMRC, Tr. Com]
Fixed point implementation [ICASSP, SPIE]
Parallel architecture [Asilomar]
Joint detection and decoding [Globecom,Tr. Com]
Suboptimal decoding algorithm [Asilomar, Tr. Inf. Th.]

38. Future research Wireless Cellular Ad-hoc Network Wireless LAN
Bluetooth/
Home Networks
Wireless LAN

39. Future research Universal wireless receiver Reconfigurable solution
Power efficient
Automate design?
Network level interaction
Resource allocation
Quality of service guarantee
Application level interaction

40. Further details http://www.ece.rice.edu/~suman

41. UZ Method

42. System Model - Received Signal
tk,p = q + g (integer and fraction part of delay)
bit i = +1
bit i+1 = +1 q g
ri(m) =
wk,p rk,p(m) g
Right +
wk,p rk,p(m) (1-g) +
wk,p rk,p(m) g
Left +
wk,p rk,p(m) (1-g)
Chip Asynchronous

43. System Model - Received Signal
A(m) = [a1R a1L … akR akL … aKR aKL]
Tc: chip period; t/Tc=q+g (integer and fraction part)
Columns of A(m): linear combinations of ck[q]-s

44. Channel Response Model
Hence, columns of A(m) for each user k :
akR = UkR zk(m) , akL = UkL zk(m)
where,
UkR = [ckR[0] … ckR[q] … ckR[N-1]]
UkL = [ckL[0] … ckL[q] … ckL[N-1]]
zk(m) = hk o pk(m)
spreading code shifted by delay
multipath attenuation and delay components
array response components

45. System Model - Received Signal
Structure of pk(m) and hk:
Path1
qk,1th element
(qk,1+1)th
qk,Pth element
(qk,P+1)th :
wk,1(1-gk,1)
wk,1 gk,1
wk,P (1-gk,P)
wk,P gk,P :
rk,1,(m)
rk,1 (m)
rk,P (m)
rk,P(m)
hk =
pk (m) =

46. Channel Estimation - Maximum Likelihood Algorithm
U: spreading codes of all the users (known)
Z: all unknown parameters of all paths of all users
time delay, attenuation, array response
Goal: Estimate Z using spreading codes and preamble

47. Channel estimation - Maximum Likelihood Algorithm
Given: L observations r1,r2, …,rL.
Joint conditional probability density function of r1,r2,…,rL
Goal: Maximize above w. r. t. channel parameters (Z).

48. Multi-step Optimization Process
Define y = UZ. Form ML estimate y, of y.
Estimate zk by a least squares fit between y=UZ and y.
Extraction of individual parameters from zk-s ^ ^ ^

49. Kronecker algorithm

50. Iterative methods To solve Rb = y Solution at step k is bk
Calculate error ek = Rbk - y
Modify solution from error and earlier estimate
Cost
matrix-vector product takes O(n2) operations
Each iteration takes O(n2) steps
Can we do better?

51. Matrix vector product Circulant matrix diagonalized by Fourier matrix
C x = (F t L F) x
Matrix vector product through Fourier transforms
Takes O(n log n) steps.
To calculate Ax when A is Toeplitz
Embed Toeplitz matrix in a circulant system
Compute product by Fourier transforms

52. Example

53. Outline of the algorithm
Correlation matrix is block-Toeplitz
Approximate it as a block-circulant system
Shift matrix as a building block
Kronecker representation of the system
Fourier transform to convert it to a block-diagonal system

54. Shift matrix Shift matrix Fourier matrix diagonalizes shift matrix:
F t s F = D F t s2 F = D2

55. In search of efficient solvers
Correlation matrix is block-Toeplitz
Rewrite correlation matrix as
RN1 - block-circulant

56. Kronecker product representation
Kronecker product is defined by
Thus

57. Kronecker algorithm The system is a sum of Kronecker products
Property of Kronecker product
Thus
is a block diagonal system

58. Architectural mapping

59. Computations Involved
delay ri bi
bi-1
time
Model
Compute Correlation Matrices
Bits of K async. users aligned at times I and I-1
Received bits of spreading length N for K users

60. Solve for the channel estimate, Ai
Multishot Detection
Solve for the channel estimate, Ai
Multishot Detection

61. Differencing Multistage Detection
Successive Stages
S=diag(AHA)
y - soft decision
d - detected bits
(hard decision)

62. Block Bi-Diagonal Matrix
Structure of AHA
Block Bi-Diagonal Matrix

63. Correlation Matrices (Per Bit)
Task Decomposition
Block I
Block II
Block III
Task B
Correlation Matrices (Per Bit)
Inverse
Matrix Products
Block IV M
U X d
A0HA1
O(K2N)
Multistage Detection
(Per Window)
Rbr[R]
O(KN)
RbbAH
= Rbr[R]
O(K2N) b
A0HA0
O(K2N)
Rbr[I]
O(KN)
Data’ M
U X
RbbAH
= Rbr[I]
O(K2N) d
O(DK2Me)
Rbb
O(K2)
A1HA1
O(K2N)
Pilot
AHr
O(KND)
Data
Channel Estimation
Multistage Detection
Task A

64. Sequential / Pipeline A B
Task A
Block IV
AHr
O(KND) d
Data
O(DK2Me)
Task B

65. (Parallel A) B Task A Task B 3367*Me cycles 885 cycles Block IV AHr
O(ND) 1
Data
O(DK2Me) d K
Task B
3367*Me cycles
885 cycles

66. At this step Task A Task B Multistage Detection Block I &II 1 Data K
Stage Stage Stage3…
Block IV
Block III
Task B

67. Joint detection and decoding

68. Convolutional codes Rate : 1/2 memory (k) : 2 d2 = d1 d4 = d1 + d3b
deven
dodd
Rate : /2
memory (k) : 2
d2 = d1
d4 = d1 + d3
d6 = d1 + d3 + d5
d8 = d3 + d5 + d7
d10 = d5 + d7 + d9
dodd
systematic bits
deven
parity bits

69. Iterative Interference Cancellation^ d2
MF for user 2
spread -
Estimate coded bits
. ..
. .. +
MF for user 1 r - y1 ^
MF for user K +
spread ^
Estimate coded bits dK dK ^ d1
Iterate the process among users

70. Interference Cancellation
User of concern c, interfering users I
r = ScAcdc + SIAIdI + z
Estimate dI
Eliminate interference
Estimate dc ^
^ yc
= STc(r- SIAIdI)

71. Prior Updates + . .. . .. - - Updated prior p(d1) from previous step
MF for user 2
spread - y1 ^
Estimate coded bits
Estimate coded bits
. ..
. .. +
MF for user 1 r -
MF for user 1 +
spread ^ dK ^ ^
p(d1|y1), d1
Prior p(d1) for next step

72. Algorithm Start with uniform prior p0(dc) for all users
Obtain an initial estimate d0 from matched filter output
In the ith iteration,
for all users, compute:
Calculate dic and pi(dc| )
Use pi(dc| ) as the prior pi+1(dc)
Stop iteration when no further change in d ^
^ yic
= S’c(r- SIAIdi-1I) ^
^ yic
^ yic

73. Convergence Study
Optimal performance achieved after a few iterations

74. Maximum weight basis decoding

75. Suboptimal single user channel decoder
y = (y1, …yN)
d = (d1, …dN)
Viterbi algorithm:
Complexity grows exponentially with k
If no codeword constraint d = sgn(y)
Estimated d may not be a codeword !!

76. Maximum weight basis decoding
More variables than equations
NR independent variables
N: block-length
R: Rate
Choice depends on yi
y= d = 1
y= d = -1
y = d = ?
d2 = d1
d4 = d1 + d3
d6 = d1 + d3 + d5
d8 = d3 + d5 + d7
d10 = d5 + d7 + d9
Want to choose maximally independent subset with largest total weight

77. Selection of maximally independent subset
Set I =
Given y, sort the weights |yi | : i = {1..N}
While | I | < NR
Choose location from {1..N} with largest weight such that I U e is still an independent subset of {1..N}
Set I = I U e .

78. Suboptimal decoding algorithm
Chose M maximum independent subset
For each independent subset
Compute the codeword dI
Compute the likelihood p ( y|dI )
Chose codeword with largest likelihood
Decoding complexity reduced from O(2k) to O(k2)
If de = sgn(ye)

79. Complexity Issues Iterative detection and decoding
Linear complexity in the number of users
Viterbi decoding for each user
Exponential complexity in the constraint length k
Cannot use large constraint length codes for real time systems

80. Suboptimal Channel Decoder
Received signal r
Select codeword d which has the largest likelihood.
If no codeword constraint d = sgn(r)
Complexity independent of k
Systematic code d = (ds,dp)
ds can be chosen in an unconstrained manner
Choice of ds uniquely determines dp

81. Suboptimal Channel Decoder (cont.)
(2,3) even parity code
code bits
transmitted bits
received signal
Pr(d=1|r=7.5) = 1
Pr(d=1|r=0.5) = 0.6
ML decoder
likelihood = (1)x(0.4)x(1) = 0.4
Unconstrained detection
likelihood = (1)x(0.6)x(1) = high !

82. Suboptimal Channel Decoder (cont.)
code bits
received signal
decide based on info bits
likelihood = (1)x(0.6)x(0) = 0 possible error!
Chose top 2 paths
likelihood = (1)x(0.4)x(1) = 0.4
Final decision based on likelihood value

83. Suboptimal Channel Decoder (cont.)
Any 2 of the 3 bits can be chosen independently
That uniquely determines the third bit.
code bits
received signal
Should first detect

84. Suboptimal Convolutional Decoder
Convolution code of rate R and block length N
NR bits can be chosen independently
Choice of NR bits not as simple
Choose the ones we believe in most
Choose the bits bi with largest received |ri|

85. Algorithm Analysis
Algorithm gives maximal independent subset with largest weight.
Complexity
Radix sort O(N)
at most k equations for each unknown
Total algorithm complexity O(NKk)