| 1. |
- Agrell, Erik, 1965, et al.
(författare)
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Gray coding for multilevel constellations in Gaussian noise
- 2007
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 53:1, s. 224-235
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Tidskriftsartikel (refereegranskat)abstract
- The problem of finding the optimal labeling (bit-to-symbol mapping) of multilevel coherent phase shift keying (PSK), pulse amplitude modulation (PAM), and quadrature amplitude modulation (QAM) constellations with respect to minimizing the bit-error probability (BEP) over a Gaussian channel is addressed. We show that using the binary reflected Gray code (BRGC) to label the signal constellation results in the lowest possible BEP for high enough signal energy-to-noise ratios and analyze what is "high enough"in this sense. It turns out that the BRGC is optimal for PSK and PAM systems whenever the target BEP is at most a few percent, which covers most systems of practical interest. New and simple closed-form expressions are presented for the BEP of PSK, PAM, and QAM using the BRGC. © 2007 IEEE.
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| 2. |
- Agrell, Erik, 1965, et al.
(författare)
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On the optimality of the binary reflected Gray code
- 2004
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 50:12, s. 3170-3182
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Tidskriftsartikel (refereegranskat)abstract
- This paper concerns the problem of selecting a binary labeling for the signal constellation in M-PSK, M-PAM, and M-QAM communication systems. Gray labelings are discussed and the original work by Frank Gray is analyzed. As is noted, the number of distinct Gray labelings that result in different bit-error probability grows rapidly with increasing constellation size. By introducing a recursive Gray labeling construction method called expansion, the paper answers the natural question of what labeling, among all possible constellation labelings, will give the lowest possible average probability of bit errors for the considered constellations. Under certain assumptions on the channel, the answer is that the labeling proposed by Gray, the binary reflected Gray code, is the optimal labeling for all three constellations, which has, surprisingly, never been proved before.
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| 3. |
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| 4. |
- Agrell, Erik, 1965, et al.
(författare)
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The binary reflected Gray code is optimal for M-PSK
- 2004
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Ingår i: Proc. IEEE International Symposium on Information Theory, Chicago, Illinois, USA. - 0780382803 ; , s. 164-
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Konferensbidrag (refereegranskat)abstract
- This paper is concerned with the problem of selecting a binary labeling for the signal constellation in an M-PSK communication system. A good starting point is labelings having the Gray property, but this is not altogether enough, since the number of distinct Gray labelings that result in different bit error probability grows rapidly with increasing constellation size. By introducing a recursive Gray labeling construction method called expansion, the paper answers the natural question of what labeling, among all possible constellation labelings (not only Gray), that will give the lowest possible average probability of bit errors. Under certain assumptions on the channel, the answer is that the labeling originally proposed by Gray, the binary reflected Gray code, is the optimal labeling for M-PSK systems, which has, surprisingly, never been proved before.
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| 5. |
- Haghighi, Kasra, 1978, et al.
(författare)
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An LLR-based Cognitive Transmission Strategy for Higher Spectrum Reutilization
- 2011
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Ingår i: IEEE GLOBECOM 2011 - Cognitive Radio and Networks Symposium. - 9781424492688
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Konferensbidrag (refereegranskat)abstract
- Reutilization of the spectrum licensed to services with low occupancy is of great interest for cognitive radios (CRs). To achieve this goal, we introduce a simple hidden Markov model which captures the primary users activity, signal uncertainties, and noise. For evaluating the performance of any CR, two new criteria are presented entitled spectrum utilization ratio (UR) and interference ratio (IR). Based on this model and new measures, a new a-posterior log-likelihood-ratio based CR is designed and implemented. Its performance is compared with standard energy-detection based spectrum-sensing CR. We demonstrate more than 300% increase in UR for up to 1% allowed interference at the SNR of -5dB.
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| 6. |
- Haghighi, Kasra, 1978, et al.
(författare)
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On Optimum Causal Cognitive Spectrum Reutilization Strategy
- 2012
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Ingår i: IEEE Journal on Selected Areas in Communications. - 0733-8716 .- 1558-0008. ; 30:10, s. 1911-1921
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study opportunistic transmission strategies for cognitive radios (CR) in which causal noisy observation from a primary user(s) (PU) state is available. PU is assumed to be operating in a slotted manner, according to a two-state Markov model. The objective is to maximize utilization ratio (UR), i.e., relative number of the PU-idle slots that are used by CR, subject to interference ratio (IR), i.e., relative number of the PU-active slots that are used by CR, below a certain level. We introduce an a-posteriori LLR-based cognitive transmission strategy and show that this strategy is optimum in the sense of maximizing UR given a certain maximum allowed IR. Two methods for calculating threshold for this strategy in practical situations are presented. One of them performs well in higher SNRs but might have too large IR at low SNRs and low PU activity levels, and the other is proven to never violate the allowed IR at the price of a reduced UR. In addition, an upper-bound for the UR of any CR strategy operating in the presence of Markovian PU is presented. Simulation results have shown a more than 116% improvement in UR at SNR of -3dB and IR level of 10% with PU state estimation. Thus, this opportunistic CR mechanism possesses a high potential in practical scenarios in which there exists no information about true states of PU.
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| 7. |
- Haghighi, Kasra, 1978, et al.
(författare)
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Sensing or Transmission: Causal Cognitive Radio Strategies with Censorship
- 2014
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Ingår i: IEEE Transactions on Wireless Communications. - 1558-2248 .- 1536-1276. ; 13:6, s. 3031-3041
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Tidskriftsartikel (refereegranskat)abstract
- This paper introduces a novel opportunistic transmission strategy for cognitive radios (CRs). The primary user (PU) is assumed to transmit in a time-slotted manner according to a two-state Markov model, and the CR is either sensing, that is, obtaining a causal, noisy observation of a primary user (PU) state, or transmitting, but not both at the same time. In other words, the CR observations of the PU are censored whenever the CR is transmitting. The objective of the CR transmission strategy is to maximize the utilization ratio (UR), i.e., the relative number of the PU-idle slots that are used by the CR, subject to that the interference ratio (IR), i.e., the relative number of the PU-active slots that are used by the CR, is below a certain level. We introduce an a-posteriori LLR-based CR transmission strategy, called CLAPP, and evaluate this strategy in terms of the achievable UR for different PU model parameters and received signal-to-noise ratios (SNRs). The performance of CLAPP is compared with a simple censored energy detection scheme. Simulation results show that CLAPP has 52% gain in UR over the best censored energy detection scheme for a maximum IR level of 10% and an SNR of -2dB. © 2002-2012 IEEE.
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| 8. |
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| 9. |
- Lassing, Johan, 1973, et al.
(författare)
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Computation of the Exact Bit-Error Rate of Coherent M-ary PSK With Gray Code Bit Mapping
- 2003
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Ingår i: IEEE Transactions on Communications. - 0090-6778 .- 1558-0857. ; 51:11, s. 1758-1760
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Tidskriftsartikel (refereegranskat)abstract
- The problem of calculating the average bit-error probability (BEP) of coherent M-ary phase-shift keying (PSK) over a Gaussian channel has been studied previously in the literature. A solution to the problem for systems using a binary reflected Gray code (BRGC) to map bits to symbols was first presented by Lee. In this letter, we show that the results obtained by Lee are incorrect for M greater than or equal to 16. We show that the reason for this is an invalid assumption that the bit-error rate (BER) is independent of the transmitted symbols, an assumption which has also propagated to textbooks. We give a new expression for the BER of M-PSK systems using the BRGC and compare this with Lee's results.
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| 10. |
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