In this paper, silver codeword modulation for a single-input single-output (SISO) system is proposed. The conventional silver code employs a pair of transmit antennas to convey two pairs of silver code super-symbols over two consecutive time slots. Similar to the golden code, the silver code is a full-rate, full-diversity space-time block code. To enable the use of a single transmit antenna for the silver code, we propose a simple encoding which produces four super-symbols that are transmitted over four consecutive time-slots. Essentially, this corresponds to the transmission of four input symbols over four time slots via a single antenna, hence maintaining the full-rate property of the conventional silver code. We generalize the scheme to transmission over K time slots, where K is a positive integer multiple of four. The encoding further ensures that all K input symbols are transmitted at least once in each of the K time slots. The error performance of the proposed scheme is significantly superior to that of an equivalent single transmit antenna golden codeword modulation scheme for a single receive antenna. For example, a signal-to-noise ratio (SNR) gain of approximately 6.5 dB is yielded for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11235_2025_1321_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">$K=4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> and 4-ary quadrature amplitude modulation at a bit error rate of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11235_2025_1321_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$10^{-6}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>. We formulate the theoretical average bit error probability for the proposed scheme, which is closely validated by simulation results. With the objective of motivating future work in the context of application of the proposed scheme to reconfigurable intelligent surfaces (RISs), we further demonstrate that substantial savings in transmit power can be realized when the proposed scheme is applied to a SISO over-the-air RIS index modulation scheme.

Silver codeword modulation for a SISO system and its application to over-the-air-RIS-IM

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2025年6月23日

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Narushan Pillay,
Hongjun Xu

摘要

In this paper, silver codeword modulation for a single-input single-output (SISO) system is proposed. The conventional silver code employs a pair of transmit antennas to convey two pairs of silver code super-symbols over two consecutive time slots. Similar to the golden code, the silver code is a full-rate, full-diversity space-time block code. To enable the use of a single transmit antenna for the silver code, we propose a simple encoding which produces four super-symbols that are transmitted over four consecutive time-slots. Essentially, this corresponds to the transmission of four input symbols over four time slots via a single antenna, hence maintaining the full-rate property of the conventional silver code. We generalize the scheme to transmission over K time slots, where K is a positive integer multiple of four. The encoding further ensures that all K input symbols are transmitted at least once in each of the K time slots. The error performance of the proposed scheme is significantly superior to that of an equivalent single transmit antenna golden codeword modulation scheme for a single receive antenna. For example, a signal-to-noise ratio (SNR) gain of approximately 6.5 dB is yielded for $K=4$ $K = 4$ and 4-ary quadrature amplitude modulation at a bit error rate of $10^{-6}$ $10^{- 6}$ . We formulate the theoretical average bit error probability for the proposed scheme, which is closely validated by simulation results. With the objective of motivating future work in the context of application of the proposed scheme to reconfigurable intelligent surfaces (RISs), we further demonstrate that substantial savings in transmit power can be realized when the proposed scheme is applied to a SISO over-the-air RIS index modulation scheme.