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Low-Resolution Quantization in Phase Modulated Systems: Optimum Detectors and Error Rate Analysis
Signal Processing · Submitted 28 Feb 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is shown that a transceiver architecture with n-bit quantization is asymptotically optimum in terms of communication reliability if n is greater than or equal to log_2(M +1).
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The abstract, sentence by sentence
This paper considers a wireless communication system with low-resolution quantizers, in which transmitted signals are corrupted by fading and additive noise. For such wireless systems, a universal lower bound on the average symbol error probability (SEP), correct for all M-ary modulation schemes, is obtained when the number of quantization bits is not enough to resolve M signal points. In the special case of M-ary phase shift keying (M-PSK), the optimum maximum likelihood detector for equi-probable signal points is derived. Utilizing the structure of the derived optimum receiver, a general average SEP expression for M-PSK modulation with n-bit quantization is obtained when the wireless channel is subject to fading with a circularly-symmetric distribution. Adopting this result for Nakagami-m fading channels, easy-to-evaluate expressions for the average SEP for M-PSK modulation are further derived. It is shown that a transceiver architecture with n-bit quantization is asymptotically optimum in terms of communication reliability if n is greater than or equal to log_2(M +1). That is, the decay exponent for the average SEP is the same and equal to m with infinite-bit and n-bit quantizers for n is greater than or equal to log_2(M+1). On the other hand, it is only equal to half and 0 for n = log_2(M) and n < log_2(M), respectively. An extensive simulation study is performed to illustrate the derived results and energy efficiency gains obtained by means of low-resolution quantizers.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This paper considers a wireless communication system with low-resolution quantizers, in which transmitted signals are corrupted by fading and additive noise. | background 0.97 | 0.29 | 0.02 | asserted 0.96 |
| s1 | For such wireless systems, a universal lower bound on the average symbol error probability (SEP), correct for all M-ary modulation schemes, is obtained when the number of quantization bits is not enough to resolve M signal points. | result 0.89 | 0.91 | 0.18 | asserted 1.00 |
| s2 | In the special case of M-ary phase shift keying (M-PSK), the optimum maximum likelihood detector for equi-probable signal points is derived. | contribution 0.64 | 0.96 | 0.05 | asserted 1.00 |
| s3 | Utilizing the structure of the derived optimum receiver, a general average SEP expression for M-PSK modulation with n-bit quantization is obtained when the wireless channel is subject to fading with a circularly-symmetric distribution. | result 0.58 | 0.95 | 0.08 | asserted 1.00 |
| s4 | Adopting this result for Nakagami-m fading channels, easy-to-evaluate expressions for the average SEP for M-PSK modulation are further derived. | result 0.58 | 0.95 | 0.06 | asserted 1.00 |
| s5 | It is shown that a transceiver architecture with n-bit quantization is asymptotically optimum in terms of communication reliability if n is greater than or equal to log_2(M +1). | result 0.97 | 0.92 | 0.60 | asserted 1.00 |
| s6 | That is, the decay exponent for the average SEP is the same and equal to m with infinite-bit and n-bit quantizers for n is greater than or equal to log_2(M+1). | result 0.52 | 0.91 | 0.30 | asserted 1.00 |
| s7 | On the other hand, it is only equal to half and 0 for n = log_2(M) and n < log_2(M), respectively. | result 0.99 | 0.90 | 0.14 | asserted 1.00 |
| s8 | An extensive simulation study is performed to illustrate the derived results and energy efficiency gains obtained by means of low-resolution quantizers. | method 0.65 | 0.96 | 0.04 | asserted 0.96 |
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Original abstract
This paper considers a wireless communication system with low-resolution quantizers, in which transmitted signals are corrupted by fading and additive noise. For such wireless systems, a universal lower bound on the average symbol error probability (SEP), correct for all M-ary modulation schemes, is obtained when the number of quantization bits is not enough to resolve M signal points. In the special case of M-ary phase shift keying (M-PSK), the optimum maximum likelihood detector for equi-probable signal points is derived. Utilizing the structure of the derived optimum receiver, a general average SEP expression for M-PSK modulation with n-bit quantization is obtained when the wireless channel is subject to fading with a circularly-symmetric distribution. Adopting this result for Nakagami-m fading channels, easy-to-evaluate expressions for the average SEP for M-PSK modulation are further derived. It is shown that a transceiver architecture with n-bit quantization is asymptotically optimum in terms of communication reliability if n is greater than or equal to log_2(M +1). That is, the decay exponent for the average SEP is the same and equal to m with infinite-bit and n-bit quantizers for n is greater than or equal to log_2(M+1). On the other hand, it is only equal to half and 0 for n = log_2(M) and n < log_2(M), respectively. An extensive simulation study is performed to illustrate the derived results and energy efficiency gains obtained by means of low-resolution quantizers.
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It is observed that a transceiver architecture with n-bit quantization is asymptotically optimum in terms of communication reliability if n is greater than or equal to log_2(M +1).
Phase Modulated Communication with Low-Resolution ADCs · 1.00
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