Minimum Mean-Squared Error Iterative Successive Parallel Arbitrated Decision Feedback Detectors for DS-CDMA Systems
Summary (3 min read)
Introduction
- This is a repository copy of Minimum mean-squared error iterative successive parallel arbitrated decision feedback detectors for DS-CDMA systems.
- The multistage or iterative DF schemes presented in [14], [15] are based on the combination of SDF and P-DF schemes in multiple stages in order to refine the symbol estimates, resulting in improved performance over conventional S-DF, P-DF and mitigation of error propagation.
II. DS-CDMA SYSTEM MODEL
- Let us consider the uplink of a symbol synchronous binary phase-shift keying (BPSK) DS-CDMA system with K users, N chips per symbol and Lp propagation paths.
- It should be remarked that a synchronous model is assumed for simplicity, although it captures most of the features of more realistic asynchronous models with small to moderate delay spreads.
- The baseband signal transmitted by the k-th active user to the base station is given by xk(t) =.
- Assuming that the receiver is synchronised with the main path, the coherently demodulated composite received signal is r(t) = K ∑ k=1 Lp−1 ∑ l=0 hk,l(t)xk(t − τk,l) + n(t) (2) where hk,l(t) and τk,l are, respectively, the channel coefficient and the delay associated with the l-th path and the k-th user.
- The MAI comes from the non-orthogonality between the received signature sequences, whereas the ISI span Ls depends on the length of the channel response, which is related to the length of the chip sequence.
III. MMSE DECISION FEEDBACK RECEIVERS
- Let us describe in this section the design of synchronous MMSE decision feedback detectors.
- In particular, the feedback filter fk(i) of user k has a number of non-zero coefficients corresponding to the available number of feedback connections for each type of cancellation structure.
- D} (8) where the two sets D and U correspond to detected and undetected users, respectively.
- In order to design the S-DF receivers and satisfy the constraints of the SDF structure, the designer must obtain the vector with initial decisions b̂(i) = sgn[ℜ(WH(i)r(i))] and then resort to the following cancellation approach.
IV. SUCCESSIVE PARALLEL ARBITRATED DF AND ITERATIVE DETECTION
- The authors present a novel interference cancellation structure and describe a low complexity near-optimal ordering algorithm that employs different orders of cancellation and then selects the most likely symbol estimate.
- The proposed ordering algorithm is compared with the optimal user ordering algorithm, which requires the evaluation of K! different cancellation orders and turns out to be too complex for practical use.
- The new receiver structure, denoted successive parallel arbitrated DF (SPA-DF) detection, is then combined with iterative cascaded DF stages [14], [15] to further refine the symbol estimates.
- The motivation for the novel DF structures is to mitigate the effects of error propagation often found in P-DF structures [14], [15], that are of great interest for uplink scenarios due to its capability of providing uniform performance over the users.
A. Successive Parallel Arbitrated DF Detection
- The idea of parallel arbitration is to employ successive interference cancellation (SIC) to rapidly converge to a local maximum of the likelihood function and, by running parallel branches of SIC with different orders of cancellation, one can arrive at sufficiently different local maxima [16].
- The rationale for this approach is to shift the ordering and attempt to benefit a given user or group of users for each decoding branch.
- The SPA-DF system employs the same filters, namely W and F, of the traditional S-DF structure and requires additional arithmetic operations to compute the parallel arbitrated candidates.
- The role of reversing the cancellation order in successive stages is to equalize the performance of the users over the population or at least reduce the performance disparities.
V. SUCCESSIVE PARALLEL ARBITRATED DF AND ITERATIVE DETECTION FOR CODED SYSTEMS
- This section is devoted to the description of the proposed SPA-DF detector and iterative detection schemes for coded systems which employ convolutional codes with Viterbi and turbo decoding.
- Specifically, the authors present iterative DF detectors based on the proposed SPA-DF structure which exploits user ordering and combine the SPA-DF with either the S-DF, the P-DF or another SPA-DF in the second stage.
- The authors show that a reduced number of turbo iterations can be used with the proposed iterative detector when a near-optimal user ordering is employed and that savings in transmitted power are also obtained as compared to previously reported turbo detectors [19]-[23].
C. Extensions
- Here, the authors briefly comment on how the proposed receiver structures can be extended to take into account asynchronous systems, dynamic scenarios, other types of communications systems and multiple access techniques.
- For asynchronous systems with large relative delays amongst the users, the observation window of each user should be expanded in order to consider an increased number of samples derived from the offsets amongst users.
- These remedies imply in augmented filter lengths and consequently increased computational complexity.
- An extension with low complexity turbo schemes such as the one in [26] are also possible with the structures presented in this paper.
- For dynamic channels that are subject to fading, the designer can rely on adaptive signal processing techniques and make the proposed detector structures adaptive in order to track the variations of the channel and the interference.
VI. SIMULATIONS
- The authors evaluate the performance of the iterative arbitrated DF structures introduced in Section IV and compare them with other existing structures.
- In the following experiments, averaged over 200 runs for uncoded systems, over 2000 for encoded systems with Viterbi decoding and over 20000 for turbo decoded schemes, it is indicated the receiver structure (linear or decision feedback (DF)).
- The results for a system with N = 32, depicted in Fig. 4 indicate that the best performance is achieved with the novel ISPASPA-DF (the SPA-DF is employed in two cascaded stages), followed by the new ISPAP-DF, the existing ISP-DF [14], the ISPAS-DF, the SPA-DF, the P-DF, the ISS-DF, the S-DF and the linear detector.
- Moreover, the performance advantages of the ISPASPA-DF and ISPAP-DF systems are even more pronounced over the other analyzed schemes for larger systems.
- Users with the first indices and poorer performance should be allocated to voice services, while the users with better performance should be designated to data transmission services that require improved QoS.
VII. CONCLUSIONS
- A novel SPA-DF structure and a low complexity nearoptimal ordering algorithm were presented and combined with iterative techniques for use with cascaded DF stages for mitigating the deleterious effects of error propagation.
- The proposed SPA-DF and iterative receivers for DS-CDMA systems were investigated in an uplink scenario and compared to existing schemes in the literature.
- The approximate MMSE in (47) is also proportional to the number of undetected users expressed by the covariance matrix RUl , but can benefit from different groups of undetected users, by selecting the undetected group of users that yield smaller MSE, resulting in better performance.
- Here, the authors mathematically discuss the MMSE of S-DF detectors with the optimal ordering algorithm.
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Citations
236 citations
Cites background from "Minimum Mean-Squared Error Iterativ..."
...However, these decision-driven detection algorithms suffer from error propagation and performance degradation....
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183 citations
Cites background from "Minimum Mean-Squared Error Iterativ..."
...These systems implemented with direct-sequence (DS) signaling are found in third-generation cellular telephony [7]–[9], indoor wireless networks [10], satellite communications, and ultrawideband technology [11] and are being considered for future systems with multicarrier (MC) versions such as MC-CDMA and MC-DS-CDMA [12] and in conjunction with multiple antennas [13]....
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...The structure of the M × L matrices C̄k, Ck, and C̃k is detailed in [9]....
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181 citations
Cites methods from "Minimum Mean-Squared Error Iterativ..."
...The DF strategy that is adopted in this paper is the parallel scheme reported in [9] and [ 13 ], which first obtains the decision vector ˆ xT,j[i] with linear equalization and then employs ˆ xT,j[i] to cancel the interference that is caused by the interfering streams....
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163 citations
Cites methods from "Minimum Mean-Squared Error Iterativ..."
...When channel state information (CSI) is available at the receiver, this interference can be mitigated by the use of successive interference cancelation (SIC) and equivalent techniques, such as the vertical Bell-Labs layered space–time and multibranch implementations [11]–[15]....
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158 citations
References
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...Recently, Verdu and Shamai [7] and Rapajic [8]et al. have investigated the information theoretic trade-off between the spectral and power efficiency of linear and non-linear multiuser detectors in synchronous AWGN channels....
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...This extrinsic information is the information about the code bit bk(i) obtained from the prior information about the other code bits λp1[bk(j)], j = i [22]....
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...This assumption is reasonable when there are many active users, has been used in previous works [15],[22]-[23] and provides an efÞcient and accurate way of computing the extrinsic information....
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"Minimum Mean-Squared Error Iterativ..." refers background in this paper
...This fact has motivated the development of various sub-optimal strategies: the linear [3] and decision feedback (DF) [4] receivers, the successive interference canceller [5] and the multistage detector [6]....
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Frequently Asked Questions (17)
Q2. What is the motivation for the proposed encoded structure?
The motivation for the proposed encoded structure is that significant gains can be obtained from iterative techniques with soft cancellation methods and error control coding [17]-[23] and from efficient receivers structures and ordering algorithms such as the novel SPA-DF detector.
Q3. What is the role of reversing the cancellation order in successive stages?
The role of reversing the cancellation order in successive stages is to equalize the performance of the users over the population or at least reduce the performance disparities.
Q4. What is the feedback filter fk(i) of user k?
In particular, the feedback filter fk(i) of user k has a number of non-zero coefficients corresponding to the available number of feedback connections for each type of cancellation structure.
Q5. How many users can be supported in comparison with the ISP-DF?
The ISPAP-DF scheme can save up to 1.4 dB and support up to 8 more users in comparison with the ISP-DF for the same BER performance.
Q6. How many additional users can be supported in comparison with the ISP-DF?
the ISPASPA-DF detector can save up to 1.8 dB and support up to 10 additional users in comparison with the ISP-DF for the same BER performance.
Q7. What is the motivation for the proposed iterative receiver structure?
2. The proposed iterative (turbo) receiver structure consists of the following stages: a soft-input-soft-output (SISO) SPA-DF detector and a maximum a posteriori (MAP) decoder.
Q8. What is the reason why the linear and P-DF detectors experience performance losses for coded?
It is worth noting that the linear and P-DF detectors experience performance losses for coded systems, relative to the other structures, as verified in [14] and which is a result of the loss in spreading gain that increases the interference power at the output of the MMSE receiver.
Q9. What is the SPA-DF receiver with hard-decision feedback?
An iterative receiver with hard-decision feedback is defined by:z(m+1)(i) = WH(i)r(i) − FH(i)b̂(m)(i) (23)where the filters W and F can be S-DF or P-DF structures, and b̂m(i) is the vector of tentative decisions from the preceding iteration that is described by:b̂(1)(i) = sgn ( ℜ [ WH(i)r(i) ])(24)b̂(m)(i) = sgn ( ℜ [ z(m)(i) ]) , m > 1 (25)where the number of stages m depends on the application.
Q10. What is the a posteriori LLR of the code bit?
The MAP decoder also computes the a posteriori LLR of every information bit, which is used to make a decision on the decoded bit at the last iteration.
Q11. What is the motivation for the proposed iterative SPA-DF receiver?
Iterative Turbo Receiver and DecodingA CDMA system with convolutional codes being used at the transmitter and the proposed iterative SPA-DF receiver with turbo decoding is illustrated in Fig.
Q12. Why do the authors adopt L = 4 for the remaining experiments?
For this reason, the authors adopt L = 4 for the remaining experiments because it presents a very attractive trade-off between performance and complexity.
Q13. What are the disadvantages of S-DF relative to PDF?
From the curves, the authors observe that a disadvantage of S-DF relative to PDF is that it does not provide uniform performance over the user population.
Q14. What is the motivation for the proposed iterative detection schemes?
The decoding of the proposed iterative detection schemes that employ the SPA-DF detector (ISPAS-DF, ISPAP-DF and ISPASPA-DF) resembles the uncoded case, where the second stage benefits from the enhanced estimates provided by the first stage that now employs convolutional codes followed by a Viterbi decoder with branch metrics based on the Hamming distance.
Q15. What is the a posteriori probability of the detector?
These estimates are used to compute the detector a posteriori probabilities P [bk(i) = ±1|z(m)k (i)] which are deinterleaved and input to the MAP decoder for the convolutionalcode.
Q16. What is the disadvantage of the SPA-DF receiver?
As occurs with S-DF receivers, a disadvantage of the SPA-DF detector is that it generally does not provide uniform performance over the user population.
Q17. What is the main feature of the proposed detectors?
This is an important feature of the proposed detectors as they can save considerable computational resources by operating with a lower number of turbo iterations.